§ 98-3 Designated firearms discharge areas.
§ 98-4 Firearms discharge and other prohibitions.
§ 98-7 Penalties for offenses.
This chapter is not intended, in any manner, to deny, misconstrue, nullify or contradict, in part or in whole, citizens' rights as given, defined and protected by the Second Amendment of the Bill of Rights of the United States Constitution.
More than 500 feet from any occupied building, dwelling or structure in use, unless you own it, and as further defined by the NYS DEC regulations for discharge of firearms and bows.
Any type device for propelling an arrow and as further defined in the NYS DEC regulations for bows, which include long, compound and recurve.
Any type rifle, shotgun, handgun or other device which uses an explosive charge to propel a missile, or missiles, through the barrel.
In personal possession afield of both firearm and ammunition, whether separate or together, so that the possessed ammunition can be chambered and fired in such gun.
A rifle as defined in § 265.00-11 of the New York Penal Law.
A shotgun as defined in § 265.00-12 of the New York Penal Law.
For the purposes of this chapter, the Town of Wheatfield shall be divided into separate designated areas, which shall be known as Firearms Discharge Areas (FDA). All firearms discharge and use of archery afield within these areas must be in accordance with federal, New York State, and local laws. These FDAs shall be defined as below:.
FDA A. That total area within the Town of Wheatfield north of the Niagara Falls Boulevard (U.S. Route 62), excluding that area with an east boundary of Ward Road (NYS 429), starting at the Niagara Falls Boulevard then north to Niagara Road, then westward back again to the Niagara Falls Boulevard.
FDA B. That total west area within the Town of Wheatfield with an east boundary of Ward Road (NYS 429), starting south at the Town line, then north to Stenzle Avenue, then west to Witmer Road, then north to the Niagara Falls Boulevard, then east to Ward Road, then north to Niagara Road, then west to the Niagara Falls Boulevard and continuing west to the Town line.
FDA C. That total area within the Town of Wheatfield south of the Niagara Falls Boulevard (U.S. Route 62), with a west boundary of Ward Road (NYS 429), starting south at the Town line, then north to Stenzle Avenue, then west to Witmer Road, then north to Niagara Falls Boulevard and continuing east to the Town line.
Editor's Note: See also the map of firearms discharge areas on file in the Town's offices.
Permitting the discharge of any rifle.
Possessing any loaded rifle afield.
Establishing, constructing, or utilizing any nonapproved rifle or other firearm range in the Town of Wheatfield.
The prohibitions of Subsection A apply.
All other firearms discharge and use of archery afield within FDA A shall be in accordance to federal, New York State and local laws.
Discharging any shotgun loaded with other than shotshell.
Permitting the discharge of any shotgun loaded with other than shotshell.
Possessing any shotgun afield loaded with other than shotshell.
All nonprohibited firearms discharge and use of archery afield shall be in accordance to federal, New York State and local laws.
Possessing any loaded firearm afield.
Discharging any firearms of any type or nature.
Any person, firm, association, or corporation exempted by the Town Board in accordance with this chapter by the issuance of a permit according to § 98-6.
Police officers, peace officers or other legal authority engaged in the performance of their duties.
Any persons or persons acting in accordance with Article 35 of the New York Penal Code.
A person, firm, association or corporation operating or utilizing a firearm range approved by the Town Board in accordance with this chapter, while on or at said range.
Editor's Note: Former Subsection E, concerning an exemption for nuisance wildlife control, which immediately followed this subsection, was deleted 11-13-2006 by L.L. No. 6-2006.
Firearms Permit Review Board (FPRB).
Be a United States citizen and resident of the Town of Wheatfield.
Have held a hunting license for at least five years.
Have a recognized knowledge of firearms and their use.
It shall be known as the Firearms Permit Review Board (FPRB). Two of its members shall be appointed as Chairman and Secretary by the Town Board, and all succeeding FPRB members shall be by recommendation from the existing FPRB to the Town Board.
To review all applications in accordance with § 98-6B and C for a firearms discharge permit (FDP) to discharge firearms and to make recommendations to the Town Board for either approval, denial or other action(s) on such application.
Review all recommendations, complaints, or charges regarding firearms discharge or use of archery afield within the Town of Wheatfield and make recommendations to the Town Board for any action(s), if any, the FPRB considers appropriate.
Make recommendations to the Town Board concerning firearms discharge and use of archery afield within the Town of Wheatfield for any actions the FPRB considers appropriate.
Any person, firm, association, or corporation with primary residence or a landowner in the Town of Wheatfield may make written application for a permit to exempt them from one or several provisions of this chapter. Application forms shall be provided according to § 98-6C.
Name(s) and age(s) of the person(s) requesting permit.
Legal resident address for each person and the length of time residing at that address.
Specific activity(s) and supporting background data for which each permit is requested.
If requested by the FPRB or Town Board, description of the area(s) where such activity(s) shall take place and include a map showing appropriate data for the area(s) requested.
If requested by the FPRB and/or Town Board, applicant tenant residents must provide a letter of permission from the landowner.
Other procedures, data, and descriptions as might be deemed appropriate by either the applicant(s), FPRB, or the Town Board.
Failure to provide required or other requested pertinent information shall be considered grounds for denial of permit.
Applications for firearms discharge permits (FDP) will be reviewed by the FPRB for evaluation and investigation. Upon completion of this initial process, the FPRB will then make recommendations to the Town Board for either approval, denial or other action(s).
The FPRB and the Town Board will act upon and complete the FDP procedure within 60 days of receiving each application.
A letter to the applicant stating the reason(s) why the application is denied or is still pending.
FDPs issued under the provisions of this chapter will expire at the end of the month two years from the date of issue.
There shall be a five-dollar fee for each permit application, new or renewal, payable at the time that each application(s) is submitted. This fee is nonrefundable.
Redress of a denied permit may be initiated 30 days after the date of denial.
All FDPs may be renewed, by application within 30 days of their expiration, by the FPRB without action by the Town Board, provided that all information stated on the original FDP application remains the same. The FPRB will notify the Town Board of all renewed FDPs.
Any violation of the provisions of this chapter shall be deemed an unclassified misdemeanor and subject to imprisonment of not more than six months in jail and a fine of not more than $1,000.


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What evidence, at a minimum, constitutes a clear and unmistakable manifestation of the parties’ intention to delegate the resolution of an arbitrability issue to an arbitrator?
Is every such delegation a delegation of an exclusive authority?
Is implied consent a sufficiently clear and unmistakable manifestation of the parties’ intention?
When (if ever) is an express statement in the arbitration agreement the minimum requisite clear and unmistakable manifestation of an intention to delegate an arbitrability issue?
When (if ever) is the incorporation of institutional arbitration procedural rules into an arbitration agreement a sufficient manifestation of the parties’ intention to delegate arbitrability issues exclusively to the arbitral tribunal?
Regarding the last of those questions, federal courts have almost uniformly opined that incorporation of institutional arbitral procedural rules that contain a provision authorizing the arbitral tribunal to determine its own jurisdiction constitutes “clear and unmistakable” evidence, within the meaning of First Options, that the parties intended to have the arbitral tribunal alone determine arbitrability issues in the first instance.
Here is his argument in brief.
The institutional arbitration rule in question -- “known in international arbitration circles as a ‘competence-competence’ [or kompetenz-kompetenz] clause” -- does not delegate exclusive authority to the arbitral tribunal to determine gateway issues of arbitrability. A typical such rule is the American Arbitration Association’s Commercial Arbitration Rule 6 that the “arbitrator shall have power to rule on his or her own jurisdiction, including any objections with respect to the existence, scope or validity of the arbitration agreement.” It does not indicate that the arbitrator’s authority to determine his/her own jurisdiction shall be exclusive, and thus does not purport to divest the courts of all authority to make such a determination.
The currently approved ALI Restatement “has concluded that the incorporation of arbitral rules like the AAA rules does not in fact constitute clear and unmistakable evidence of an intention to arbitrate arbitrability as required by First Options.” Restatement § 2-8 Reporter’s Note b(iii) (Tentative Draft No. 4, 2015). The Restatement notes that “[f]irst, and most fundamentally, the rules do not purport to give arbitrators the exclusive authority to rule on the enforceability of the arbitration agreement.” Id.
Prof. Bermann maintains that SCOTUS requires that, to constitute the clear and unmistakable evidence sufficient to rebut the presumption that arbitrability issues are for the courts to adjudicate, “the language chosen must unambiguously establish the ‘parties’ manifestation of intent’ to withdraw from courts authority to resolve issues of arbitrability.” Citing Rent-A-Center, West Inc. v. Jackson, 561 U.S. 63, 69n.1 (2010). He points out that the Rent-A-Center case identifies express language that is clear in that regard; that is, the parties agreed that the “Arbitrator, and not any federal, state or local court or agency, shall have exclusive authority to resolve any dispute relating to the interpretation, applicability, enforceability or formation of this [Arbitration] Agreement.” Id. at 66. Thus, the delegation to the tribunal was not only of primary authority, but of exclusive authority, to resolve such issues.
In contrast, institutional kompetenz-kompetenz language, as interpreted in U.S. law, confers on an arbitral tribunal an authority to determine arbitrability that is non-exclusive. Prof. Bermann points, for example, to Federal Arbitration Act (“FAA”) § 4, which authorizes federal courts to compel arbitration “upon being satisfied that the making of the agreement for arbitration . . . is not in issue.” 9 U.S.C. § 4.
swallow the rule regarding delegation.
Prof. Bermann furthermore argues that the First Options rule is that the courts have presumptive authority to determine arbitrability, and that circumstances divesting the court of such authority by delegation are anticipated to be the exception. But, he points out, “kompetenz-kompetenz provisions are ubiquitous” among the arbitration administering organizations. Therefore, he argues, if the mere adoption of the rules of one of those organizations constitutes clear and unmistakable evidence of delegation under First Options, then the exception in effect will swallow the rule.
For example, “very few international arbitrations are conducted in the absence of” the adoption of such arbitration rules, and indeed the incorporation of such rules is essentially “boiler-plate” in arbitration agreements. If such an incorporation constitutes clear and unmistakable evidence of an intention to delegate questions of arbitrability to an arbitrator, then the effect is to make delegation the rule and the court’s authority to determine questions of arbitrability in the first instance the exception.
Put another way, “[i]f ordinary kompetenz-kompetenz language found in all modern arbitral rules and all modern arbitration laws were sufficient to rebut the First Options presumption, that presumption will cease to exist.” Prof. Bermann concludes that something more must be required in order to constitute the requisite clear and unmistakable evidence of intent.
“[A] party cannot be required to submit to arbitration any dispute which he has not agreed to submit.” Howsam, 537 U.S. at 83. Prof. Bermann’s objection is that incorporation by reference of a competence-competence provision of administered arbitration rules is not a clear and unmistakable manifestation that the parties agreed to submit arbitrability questions for resolution exclusively by arbitrators in the first instance, to the exclusion of the courts.
This is certainly food for thought. On the one hand, the adoption of Prof. Bermann’s argument would likely muddy the pertinent jurisprudence and make the courts’ job relative to arbitrations more taxing. (And it would naturally add another checklist item in the drafting of arbitration agreements.) On the other hand, the argument is reasonably supported, and the advisability of adopting it arguably increases as the significance of the arbitability issue in question increases.
For example, SCOTUS has made it plain that the notion of “class arbitration” refers to a rather different procedure than standard bilateral arbitration as envisioned at the time of the enactment of the FAA. Indeed, the differences between class arbitration and ordinary arbitration -- in terms of procedural complexity, expenditure of resources, and consequences -- are enormous, and so the determination of whether an arbitration agreement permits class arbitration is profoundly important. What should be considered a “clear and unmistakable” manifestation of the parties’ mutual intention to delegate that determination exclusively to an arbitrator in the first instance? An express specific statement in that regard arguably would be best. The incorporation by reference of arbitration rules that happen to contain a kompetenz-kompetenz provision surely should not be sufficient for those purposes.
 There is an abundance of such rules, which are more or less standard in administered arbitration procedures. See, e.g., American Arbitration Association, Commercial Arbitration Rules 6; International Center for Dispute Resolution, International Dispute Resolution Procedures, Art. 19(1); ICC, Rules of Arbitration, Art. 6(3); UNCITRAL, Arbitration Rules, Art. 23(1); LCIA, Arbitration Rules, Art. 23.1; CPR, Rules for Non-Administered Arbitration of International Disputes, Art. 8.1.

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§ 354-1 Water Utility Division.
§ 354-2 Application for service; fees.
§ 354-6 Rules and regulations.
§ 354-8 Replacement of water services.
Sewers — See Ch. 277.
Management and control. Within the Department of Public Works there shall be the Water Utility Division.
Superintendent of the Water Utility Division. The Superintendent of the Water Utility Division shall be in charge of the operation of the Water Utility Division. The Superintendent of the Water Utility Division shall be appointed by the Director of the Department of Public Works subject to the provisions of Title 11A. The Superintendent of the Water Utility Division must satisfy all license and other requirements which may be imposed by any federal or state regulatory agency having jurisdiction over the operation of the City's water utility.
Editor's Note: See N.J.S.A. 11A:1-1 et seq.
Application for water service shall be made to the Tax Collector at his office in the Municipal Building. Each application shall be accompanied by payment of the connection fee, which shall be as set forth in Chapter 146, Fee Schedule, of the Code of the City of Burlington.
All uses of water shall be metered and rates for such use shall be set by the Common Council. With the exception of industrial users, bills shall be payable semiannually, on March 15 and September 15 of each year. The water rates shall be specified in Chapter 146, Fee Schedule.
Industrial users shall be billed monthly based on actual use.
Service charges, connection fees or other charges levied in accordance with N.J.S.A. 40A:31-10 and 40A:31-11, shall be a first lien or charge against the property benefitted therefrom. If any part of the amount due and payable shall remain unpaid for 30 days following the billing date interest upon the amount unpaid shall accrue at a rate of interest permitted by statute. The Common Council may authorize payment of delinquent assessments on an installment basis in accordance with N.J.S.A. 54:5-19. Liens resulting from the operation of the water utility shall be enforceable in the manner provided for real property tax liens in N.J.S.A. 54:5-1 et seq.
The Water Utility Division may discontinue service to any property for the failure to pay any amount owing within 30 days after the date the amount is due and payable, if written notice of the proposed discontinuance of service and of the reasons therefor have been given, within at least 10 days prior to the date of discontinuance, to the owner of record of the property. In the event that notice is provided by mail, the notice requirements shall be satisfied if the mailing is made to the last known address of the owner of record and is postmarked at least 10 days prior to the date of discontinuance.
Office hours. The payment of water bills shall be at the tax office at the City Hall, and the office shall be open for information, application and payment of water bills from 9:00 a.m. to 5:00 p.m., Monday through Friday, legal holidays excepted.
All road or street openings for the purpose of making water connections or repairs shall be in compliance with the provisions set forth in Chapter 306, Streets and Sidewalks, Article III, Excavations.
Installation of fixtures and piping. Installation of fixtures or piping shall be made in accordance with the provisions of the Uniform Construction Code as directed by the Construction Code Official or appropriate subcode official. Permit fees shall be established pursuant to the Uniform Construction Code as set forth in the applicable section of the New Jersey Administrative Code.
Editor's Note: See Ch. 125, Construction Codes, Uniform.
Regulations. Service shall be installed and maintained by the property owner in accordance with the standard detail on file in the Construction Code Official's office. A copy of the standard detail shall also be maintained in the office of the Municipal Clerk. Service pipe from main to building shall be Type K copper tubing, with Mueller stop and stop box inside curb, installed and maintained at the expense of the property owner.
That failure to reply will result in the imposition of fines and penalties, and may result in the water services being shut off without further notice.
Property owners shall be given no less than 10 days from the date of receipt to respond.
Follow-up notice. The City may, at its discretion, attempt additional contact with the property owner via phone, subsequent mailings, and/or in-person visits to the property.
Final notice. Should the property owner fail to respond by the required date, the City shall mail a final notice, via certified mail, that access to the property shall be required on or about a specific date, no less than seven days from the date of the final notice.
Residential meters shall not go more than 20 years without replacement.
Fines and penalties. Should the property owner fail to provide access by the date outlined within the City's final notice, or fail to otherwise comply with this section, the property owner shall be subject to fines and penalties as per § 354-9 of the City Code.
Suspected tampering of meters; irregular readings.
Any person who interferes with, changes the locations of or removes any water meter or valve or fittings connected therewith, without the permission of the Water Utility Division, shall be subject to fines and penalties as per § 354-9 of the City Code.
If a meter at any time fails to accurately record the amount of water used, the quantity shall be determined and the charge made, based on the average amount registered during such preceding period of time prior to the date of failure, as the Water Utility Division may elect.
The City shall be entitled to access any water meters based upon suspected tampering with meter equipment, irregular readings, or for other reasonable cause.
Notice of the City's need for access under this section shall not be required to state the basis of the suspected tampering, irregular reading, or other reason for requiring access.
Notice under this section shall be required to be sent within 30 days of the suspected tampering, meter alarm, irregular reading, or other cause resulting in the need for access.
If access is required under this section and the property owner and/or occupant fails to provide and/or denies access, the property owner shall be subject to fines and penalties as per § 354-9 of the City Code.
Meter testing shall be required every two to five years, at the discretion of the City Water Authority. The City shall have the right to witness tests if being performed by the property owner, and must be notified at least 30 days prior to scheduling any independent tests. All meter testing shall be performed by a New Jersey Certified Meter Tester. Notice, access, testing, and penalties shall be governed by § 354-6A and § 354-9 of the City Code.
No property governed by this section shall utilize metering equipment older than 10 years. For the first replacement of meters after the enactment of this section, the City shall bear all costs associated with replacement meter purchase and installation. All subsequent replacements shall be the sole responsibility of the property owner.
For properties governed by this section, upon receipt of notice of an irregular reading, the property owner shall be required to: (i) Respond within seven days of receipt of the notice to schedule an inspection by the City; and (ii) Complete all necessary repairs within 30 days of the City inspection, unless this time frame is waived in writing by the City Water Authority. Failure to permit inspection and remedy the condition within the required time frame shall result in fines and penalties as outlined within § 354-9 of the City Code, and shall result in the City being held harmless for any claims, damages, or other costs resulting from the condition giving rise to the need for an inspection.
Regardless of whether site plan or other Land Use Board approval is required, plans for new construction shall be submitted to the City Water Authority for review of the proposed water service size, meter size, and meter location. The City Water Authority's approval shall be required prior to the issuance of permits.
For all new construction, costs for purchase and installation of meters, as well as compliance with the City's Water Ordinance, shall be borne by the property owner.
Adjustment of charges may be made at the discretion of the Tax Collector on the personal application only of the owner of the property charged.
In addition to the fines and penalties permitted herein, the City Water Authority reserves the right to turn off the supply of water to any property for refusal or neglect to immediately repair any leaky pipe, fixture, or attachment from the main in, without provision of further notice.
All new fire services shall be metered at the time of installation. The property owner shall be responsible for the purchase, installation, testing, and maintenance of all metering equipment, subject to City Water Authority approval.
For all existing construction for which a meter for fire services is required, the City will purchase and install the required equipment. After installation is complete, the property owner shall be responsible for all testing, maintenance, replacement, and other costs and/or obligations.
The City shall annually inspect all fire services metering equipment. Fees for the annual inspection are outlined within Chapter 146 of the City Code.
The City shall read all fire meters as part of the existing commercial meter account reading schedule. Rates for usage shall be based on existing water rates at the time of the reading.
The connection fee shall be recomputed at the end of each budget year, after a public hearing is held, pursuant to the standards set forth in N.J.S.A. 40A:31-11. The revised connection fee shall be imposed upon users who subsequently connect to the system.
Purpose. In the event any City street is resurfaced or repaved, all noncopper water services shall be replaced with Type K copper tubing before such street is resurfaced or repaved.
Curb stops shall be Mueller Company No. H-15200 and stop boxes shall be Mueller Company No. H-10314, complete with rod.
Taps. All taps to the mains not exceeding one inch in diameter shall be made by the City Water Utility Division.
Any person violating any provisions of this chapter shall, upon conviction, be subject to penalties as provided in Chapter 1, Article III, General Penalty, of this Code. Each day that the violation continues shall be deemed a separate offense.


text:
at issue in Carella is a trial error subject to harmless-error analysis. The error at issue here-a misdescription of an element of the crimeis an error of omission, not an error of the structural sort that defies harmless-error analysis.
Certiorari granted; 81 F.3d 863, vacated and remanded.
A California court convicted respondent Kenneth Roy of the robbery and first-degree murder of Archie Mannix. The State's theory, insofar as is relevant here, was that Roy, coming to the aid of a confederate who was trying to rob Mannix, helped the confederate kill Mannix. The trial judge gave the jury an instruction that permitted it to convict Roy of first-degree murder as long as it concluded that (among other things) Roy, "with knowledge of" the confederate's "unlawful purpose" (robbery), had helped the confederate, i. e., had "aid[ed]," "promote[d]," "encourage[d]," or "instigate[d]" by "act or advice ... the commission of" the confederate's crime. The California Supreme Court later held in People v. Beeman, 35 Cal. 3d 547, 561, 674 P. 2d 1318, 1326 (1984), that an identical instruction was erroneous because of what it did not say, namely, that state law also required the jury to find that Roy had the "knowledge [and] intent or purpose of committing, encouraging, or facilitating" the confederate's crime. Id., at 561, 674 P. 2d, at 1326 (emphasis added). Despite this error, the California Court of Appeal affirmed Roy's conviction because it found the error "harmless beyond a reasonable doubt." See Chapman v. California, 386 U. S. 18, 24 (1967). The California Supreme Court denied postconviction relief.
Ninth Circuit panel affirmed. Roy v. Gomez, 55 F.3d 1483 (1995).
"[T]he omission is harmless only if review of the facts found by the jury establishes that the jury necessarily found the omitted element." 81 F. 3d, at 867 (emphasis in original).
As we understand that statement in context, it meant: "[T]he omission [of the 'intent' part of the instruction] is harmless only if review of the facts found by the jury [namely, assistance and knowledge] establishes that the jury necessarily found the omitted element [namely, 'intent']." Ibid.
The State of California, seeking certiorari, argues that this definition of "harmless error" is far too strict and that this Court's decisions require application of a significantly less strict "harmless error" standard in cases on collateral review. See Brecht v. Abrahamson, 507 U. S. 619 (1993); O'Neal, supra.
determination in a habeas corpus proceeding ordinarily should apply the "harmless error" standard that the Court had previously enunciated in Kotteakos v. United States, 328 U. S. 750 (1946), namely, "whether the error 'had substantial and injurious effect or influence in determining the jury's verdict.''' Brecht, supra, at 637 (citing Kotteakos, supra, at 776). The Court recognized that the Kotteakos standard did not apply to "'structural defects in the constitution of the trial mechanism, which defy analysis by "harmless-error" standards,'" 507 U. S., at 629, but held that the Kotteakos standard did apply to habeas review of what the Court called "trial errors," including errors in respect to which the Constitution requires state courts to apply a stricter, Chapmantype standard of "harmless error" when they review a conviction directly. 507 U. S., at 638. In O'Neal, supra, this Court added that where a judge, in a habeas proceeding, applying this standard of harmless error, "is in grave doubt as to the harmlessness of an error," the habeas "petitioner must win." Id., at 437.
sistent with the concurring opinion in Carella, does not, in our view, overcome the holding of Brecht, followed in O'Neal, that for reasons related to the special function of habeas courts, those courts must review such error (error that may require strict review of the Chapman-type on direct appeal) under the Kotteakos standard. Thus, we are convinced that the "harmless error" standards enunciated in Brecht and O'Neal should apply to the "trial error" before us as enunciated in those opinions and without the Ninth Circuit's modification.
For these reasons, we grant respondent's motion for leave to proceed in forma pauperis and the petition for a writ of certiorari, vacate the Ninth Circuit's determination, and remand for further proceedings consistent with this opinion.
JUSTICE SCALIA, with whom JUSTICE GINSBURG joins as to Part I, concurring.
I agree with what the Court decides in its per curiam opinion: that the Brecht-O'Neal standard for reversal of the conviction ("grave doubt as to the harmlessness of the error"), see Brecht v. Abrahamson, 507 U. S. 619 (1993), and O'Neal v. McAninch, 513 U. S. 432 (1995), rather than the more stringent Chapman standard (inability to find the error "harmless beyond a reasonable doubt"), see Chapman v. California, 386 U. S. 18 (1967), applies to the error in this case when it is presented, not on direct appeal, but as grounds for habeas corpus relief. The Ninth Circuit did not apply that more deferential standard, and I therefore concur in the remand.
v. Louisiana, 508 U. S. 275 (1993), a criminal defendant is constitutionally entitled to a jury verdict that he is guilty of the crime, and absent such a verdict the conviction must be reversed, "no matter how inescapable the findings to support that verdict might be." Id., at 279. A jury verdict that he is guilty of the crime means, of course, a verdict that he is guilty of each necessary element of the crime. United States v. Gaudin, 515 U. S. 506, 522-523 (1995). Formally, at least, such a verdict did not exist here: The jury was never asked to determine that Roy had the "intent or purpose of committing, encouraging, or facilitating" his confederate's crime. People v. Beeman, 35 Cal. 3d 547, 561, 674 P. 2d 1318, 1326 (1984).
v. McAninch, supra, at 437). That seems to me to impart to the determination a black-and-white character which it does not possess, any more than other determinations possess it. It can be "the better view," but far from "certain," that, given the facts in the record, no juror could find x without also finding y. What O'Neal means is that, when the point is arguable, the State's determination of harmless error must be sustained.
One final point: I write as I have written only because the Court has rejected the traditional view of habeas corpus relief as discretionary. See Withrow v. Williams, 507 U. S. 680,720 (1993) (SCALIA, J., concurring in part and dissenting in part). But for that precedent, I would be content to grant federal habeas relief for this sort of state-court error only when there has been no opportunity to litigate it before, or when there is substantial doubt, on the facts, whether the defendant was guilty. See ibid.

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This appendix is adapted from the original paper describing the PARSHL program  for sinusoidal modeling of audio. While many of the main points are summarized elsewhere in the text, the PARSHL paper is included here as a source of more detailed info on carrying out elementary sinusoidal modeling of sound based on the STFT.
As mentioned in §G.7.1, the phase vocoder was a widely used analysis tool for additive synthesis starting in the 1970s. A difficulty with the phase vocoder, as traditionally implemented, is that it uses a fixed uniform filter bank. While this works well for periodic signals, it is relatively inconvenient for inharmonic signals. An ``inharmonic phase vocoder'' called PARSHLH.1 was developed in 1985 to address this problem in the context of piano signal modeling . PARSHL worked by tracking peaks in the short-time Fourier transform (STFT), thereby synthesizing an adaptive inharmonic FIR filter bank, replacing the fixed uniform filter bank of the vocoder. In other respects, PARSHL could be regarded as a phase-vocoder analysis program.
The PARSHL program converted an STFT to a set of amplitude and frequency envelopes for inharmonic, quasi-sinusoidal-sum signals. Only the most prominent peaks in the spectrum of the input signal were tracked. For quasi harmonic sounds, such as the piano, the amplitudes and frequencies were sampled approximately once per period of the lowest frequency in the analysis band. For resynthesis, PARSHL supported both additive synthesis  using an oscillator bank and overlap-add reconstruction from the STFT, or both.
PARSHL followed the amplitude, frequency, and phaseH.2 of the most prominent peaks over time in a series of spectra, computed using the Fast Fourier Transform (FFT) The synthesis part of the program used the analysis parameters, or their modification, to generate a sinewave in the output for each peak track found.
Compute the STFT using the frame size, window type, FFT size, and hop size specified by the user.
Compute the squared magnitude spectrum in dB ( ).
Find the bin numbers (frequency samples) of the spectral peaks. Parabolic interpolation is used to refine the peak location estimates. Three spectral samples (in dB) consisting of the local peak in the FFT and the samples on either side of it suffice to determine the parabola used.
The magnitude and phase of each peak is calculated from the maximum of the parabola determined in the previous step. The parabola is evaluated separately on the real and imaginary parts of the spectrum to provide a complex interpolated spectrum value.
Each peak is assigned to a frequency track by matching the peaks of the previous frame with the current one. These tracks can be ``started up,'' ``turned-off'' or ``turned-on'' at any frame by ramping in amplitude from or toward 0 .
Arbitrary modifications can be applied to the analysis parameters before resynthesis.
If additive synthesis is requested, a sinewave is generated for each frequency track, and all are summed into an output buffer. The instantaneous amplitude, frequency, and phase for each sinewave are calculated by interpolating the values from frame to frame. The length of the output buffer is equal to the hop size which is typically some fraction of the window length .
Repeat from step 1, advancing samples each iteration until the end of the input sound is reached.
where denotes the FFT window, and is the hop size in samples. This constant overlap-add (COLA) constraint ensures that the successive frames will overlap in time in such a way that all data are weighted equally.
The COLA constraint can be overly conservative for steady-state signals. For additive synthesis purposes, it is more efficient and still effective to increase the hop size to the number of samples over which the spectrum is not changing appreciably. In the case of the steady-state portion of piano tones, the hop size appears to be limited by the fastest amplitude envelope ``beat'' frequency caused by mistuning strings on one key or by overlapping partials from different keys.
For certain window types (such as sum-of-cosine windows, as discussed in Chapter 3), there exist perfect overlap factors in the sense of (H.1). For example, a rectangular window can hop by , where is any positive integer, and a Hanning or Hamming window can use any hop size of the form . For the Kaiser window, in contrast, there is no perfect hop size other than .
The COLA criterion for windows and their hop sizes is not the best perspective to take when overlap-add synthesis is being constructed from the modified spectra . As discussed in Chapter 9, the hop size is the decimation factor applied to each FFT filter-bank output, and the window is the envelope of each filter's impulse response. The decimation by causes aliasing, and the frame rate is equal to twice the ``folding frequency'' of this aliasing. Consequently, to minimize aliasing, the choice of hop size should be such that the folding frequency exceeds the ``cut-off frequency'' of the window. The cut-off frequency of a window can be defined as the frequency above which the window transform magnitude is less than or equal to the worst-case side-lobe level. For convenience, we typically use the frequency of the first zero-crossing beyond the main lobe as the definition of cut-off frequency. Following this rule yields overlap for the rectangular window, overlap for Hamming and Hanning windows, and (5/6) overlap for Blackman windows. The hop size usable with a Kaiser window is determined by its design parameters (principally, the desired time-bandwidth product of the window, or, the ``beta'' parameter) .
One may wonder what happens to aliasing in the perfect-reconstruction case in which (H.1) is satisfied. The answer is that aliasing does occur in the individual filter-bank outputs, but this aliasing is canceled in the reconstruction by overlap-add if there were no modifications to the STFT. For a general discussion of aliasing cancellation in decimated filter banks, see Chapter 11 (especially §11.4.5) and/or .
The FFT size is normally chosen to be the first power of two that is at least twice the window length , with the difference filled with zeros (``zero-padded''). The reason for increasing the FFT size and filling in with zeros is that zero-padding in the time domain corresponds to interpolation in the frequency domain, and interpolating the spectrum is useful in various ways. First, the problem of finding spectral peaks which are not exact bin frequencies is made easier when the spectrum is more densely sampled. Second, plots of the magnitude of the more smoothly sampled spectrum are less likely to confuse the untrained eye. (Only signals truly periodic in samples should not be zero-padded. They should also be windowed only by the Rectangular window.) Third, for overlap-add synthesis from spectral modifications, the zero-padding allows for multiplicative modification in the frequency domain (convolutional modification in the time domain) without time aliasing in the inverse FFT. The length of the allowed convolution in the time domain (the impulse response of the effective digital filter) equals the number of extra zeros (plus one) in the zero padding.
If is the number of samples in the main lobe when the zero-padding factor is 1 ( ), then a zero-padding factor of gives samples for the same main lobe (and same main-lobe bandwidth). The zero-padding (interpolation) factor should be large enough to enable accurate estimation of the true maximum of the main lobe after it has been frequency shifted by some arbitrary amount equal to the frequency of a sinusoidal component in the input signal. We have determined by computational search that, for a rectangularly windowed sinusoid (of any frequency), quadratic frequency interpolation (using the three highest bins) yields at least (of the distance from the sinc peak to the first zero-crossing) accuracy if the zero-padding factor is 5 or higher.
Figure H.1: Illustration of the first two steps of PARSHL. (a) Input data. (b) Windowed input data. (c) FFT buffer with the windowed input data. (d) Resulting magnitude spectrum.
As mentioned in the previous section, we facilitate phase detection by using a zero-phase window, i.e., the windowed data (using an odd length window) is centered about the time origin. A zero-centered, length data frame appears in the length FFT input buffer as shown in Fig.H.1c. The first samples of the windowed data, the ``negative-time'' portion, will be stored at the end of the buffer, from sample to , and the remaining samples, the zero- and ``positive-time'' portion, will be stored starting at the beginning of the buffer, from sample 0 to . Thus, all zero padding occurs in the middle of the FFT input buffer.
Due to the sampled nature of spectra obtained using the STFT, each peak (location and height) found by finding the maximum-magnitude frequency bin is only accurate to within half a bin. A bin represents a frequency interval of Hz, where is the FFT size. Zero-padding increases the number of FFT bins per Hz and thus increases the accuracy of the simple peak detection. However, to obtain frequency accuracy on the level of of the distance from a sinc maximum to its first zero crossing (in the case of a rectangular window), the zero-padding factor required is . (Note that with no zero padding, the STFT analysis parameters are typically arranged so that the distance from the sinc peak to its first zero-crossing is equal to the fundamental frequency of a harmonic sound. Under these conditions, of this interval is equal to the relative accuracy in the fundamental frequency measurement. Thus, this is a realistic specification in view of pitch discrimination accuracy.) Since we would nominally take two periods into the data frame (for a Rectangular window), a Hz sinusoid at a sampling rate of KHz would have a period of samples, so that the FFT size would have to exceed one million. A more efficient spectral interpolation scheme is to zero-pad only enough so that quadratic (or other simple) spectral interpolation, using only bins immediately surrounding the maximum-magnitude bin, suffices to refine the estimate to accuracy. PARSHL uses a parabolic interpolator which fits a parabola through the highest three samples of a peak to estimate the true peak location and height (cf. Fig.H.2).
Figure H.2: Parabolic interpolation of the highest three samples of a peak.
Figure H.3: Coordinate system for the parabolic interpolation.
We have seen that each sinusoid appears as a shifted window transform which is a sinc-like function. A robust method for estimating peak frequency with very high accuracy would be to fit a window transform to the sampled spectral peaks by cross-correlating the whole window transform with the entire spectrum and taking and interpolated peak location in the cross-correlation function as the frequency estimate. This method offers much greater immunity to noise and interference from other signal components.
We have found empirically that the frequencies tend to be about twice as accurate when dB magnitude is used rather than just linear magnitude. An interesting open question is what is the optimum nonlinear compression of the magnitude spectrum when quadratically interpolating it to estimate peak locations.
The magnitude spectrum is used to find , but can be computed separately for the real and imaginary parts of the complex spectrum to yield a complex-valued peak estimate (magnitude and phase).
Once an interpolated peak location has been found, the entire local maximum in the spectrum is removed. This allows the same algorithm to be used for the next peak. This peak detection and deletion process is continued until the maximum number of peaks specified by the user is found.
The peak detection process returns the prominent peaks in a given frame sorted by frequency. The next step is to assign some subset of these peaks to oscillator trajectories, which is done by the peak matching algorithm. If the number of spectral peaks were constant with slowly changing amplitudes and frequencies along the sound, this task would be straightforward. However, it is not always immediately obvious how to connect the spectral peaks of one frame with those of the next.
To describe the peak matching process, let's assume that the frequency tracks were initialized at frame and we are currently at frame . Suppose that at frame the frequency values for the tracks are , and that we want to match them to the peaks, with frequencies , of frame .
12pt (1) If a match is found inside the maximum change limit, the track is continued (unless there is a conflict to resolve, as described below).
12pt (2) If no match is made, it is assumed that the track with frequency must ``turn off'' entering frame , and is matched to itself with zero magnitude. Since oscillator amplitudes are linearly ramped from one the frame to the next, the terminating track will ramp to zero over the duration of one frame hop. This track will still exist (at zero amplitude), and if it ever finds a frame with a spectral peak within its capture range , it will ``turned back on,'' ramping its amplitude up to the newly detected value. It is sometimes necessary to introduce some hysteresis into the turning on and off process in order to prevent ``burbling'' of the tracks whose peaks sometimes make the cut and sometimes don't. Normally this problem can be avoided by searching for many more spectral peaks than there are oscillators to allocate.
12pt (3) If a track finds a match which has already been claimed by another track, we give the peak to the track which is closest in frequency, and the ``losing'' track looks for another match. If the current track loses the conflict, it simply picks the best available non-conflicting peak. If the current track wins the conflict, it calls the assignment procedure recursively on behalf of the dislodged track. When the dislodged track finds the same peak and wants to claim it, it will see there is a conflict which it loses and will move on. This process is repeated for each track, solving conflicts recursively, until all existing tracks are matched or ``turned-off''.
After each track has extended itself forward in time or turned off, the peaks of frame which have not been used are considered to be new trajectories and a new track is ``started-up'' for each one of them up to the maximum number of oscillators specified (which again should be less than the number of spectral peaks detected). The new oscillator tracks are started at frame with zero magnitude and ramp to the correct amplitude at the current frame .
Once the program has finished, the peak trajectories for a sound look as in Fig.H.4.
Figure H.4: Peak trajectories for a piano tone.
The possibilities that STFT techniques offer for modifying the analysis results before resynthesis have an enormous number of musical applications. Quatieri and McAulay  give a good discussion of some useful modifications for speech applications. By scaling and/or resampling the amplitude and the frequency trajectories, a host of sound transformations can be accomplished.
Time-scale modifications can be accomplished by resampling the amplitude, frequency, and phase trajectories. This can be done simply by changing the hop size in the resynthesis (although for best results the hop size should change adaptively, avoiding time-scale modifications during voice consonants or attacks, for example). This has the effect of slowing down or speeding up the sound while maintaining pitch and formant structure. Obviously this can also be done for a time-varying modification by having a time-varying hop size . However, due to the sinusoidal representation, when a considerable time stretch is done in a ``noisy'' part of a sound, the individual sinewaves start to be heard and the noise-like quality is lost.
Frequency transformations, with or without time scaling, are also possible. A simple one is to scale the frequencies to alter pitch and formant structure together. A more powerful class of spectral modifications comes about by decoupling the sinusoidal frequencies (which convey pitch and inharmonicity information) from the spectral envelope (which conveys formant structure so important to speech perception and timbre). By measuring the formant envelope of a harmonic spectrum (e.g., by drawing straight lines or splines across the tops of the sinusoidal peaks in the spectrum and then smoothing), modifications can be introduced which only alter the pitch or only alter the formants. Other ways to measure formant envelopes include cepstral smoothing  and the fitting of low-order LPC models to the inverse FFT of the squared magnitude of the spectrum . By modulating the flattened (by dividing out the formant envelope) spectrum of one sound by the formant-envelope of a second sound, ``cross-synthesis'' is obtained. Much more complex modifications are possible.
The analysis portion of PARSHL returns a set of amplitudes , frequencies , and phases , for each frame index , with a ``triad'' ( ) for each track . From this analysis data the program has the option of generating a synthetic sound.
where is the number of tracks present at frame ; ; and is the length of the synthesis buffer (without any time scaling , the analysis hop size). To avoid ``clicks'' at the frame boundaries, the parameters ( ) are smoothly interpolated from frame to frame.
The parameter interpolation across time used in PARSHL is the same as that used by McAulay and Quatieri . Let ( ) and ( ) denote the sets of parameters at frames and for the th frequency track. They are taken to represent the state of the signal at time 0 (the left endpoint) of the frame.
where is the time sample into the th frame.
which smoothly goes from frame to frame and where each sinusoid accounts for both the rapid phase changes (frequency) and the slowly varying phase changes.
Figure H.5 shows the result of the analysis/synthesis process using phase information and applied to a piano tone.
Figure H.5: (a) Original piano tone, (b) synthesis with phase information, (c) synthesis without phase information.
A traditional result of sound perception is that the ear is sensitive principally to the short-time spectral magnitude and not to the phase, provided phase continuity is maintained. Our experience has been that this may or may not be true depending on the application, and in §H.0.9 we will discuss it. Obviously if the phase information is discarded, the analysis, the modification, and the resynthesis processes are simplified enormously. Thus we will use the magnitude-only option of the program whenever the application allows it.
In the peak detection process we calculate the magnitude and phase of each peak by using the complex spectrum. Once we decide to discard the phase information there is no need for complex spectra and we simply can calculate the magnitude of the peak by doing the parabolic interpolation directly on the log magnitude spectrum.
The synthesis also becomes easier; there is no need for a cubic function to interpolate the instantaneous phase. The phase will be a function of the instantaneous frequency and the only condition is phase continuity at the frame boundaries. Therefore, the frequency can be linearly interpolated from frame to frame, like the amplitude. Without phase matching the synthesized waveform will look very different from the original (Fig.H.5), but the sound quality for many applications will be perceptually the same.
The task of the program can be simplified and the analysis/synthesis results improved if the sound input is appropriately manipulated before running the program.
Most important is to equalize the input signal. This controls what it means to find spectral peaks in order of decreasing magnitude. Equalization can be accomplished in many ways and here we present some alternatives.
12pt (1) A good equalization strategy for audio applications is to weight the incoming spectrum by the inverse of the equal-loudness contour for hearing at some nominal listening level (e.g., dB). This makes spectral magnitude ordering closer to perceptual audibility ordering.
12pt (2) For more analytical work, the spectrum can be equalized to provide all partials at nearly the same amplitude (e.g., the asymptotic roll-off of all natural spectra can be eliminated). In this case, the peak finder is most likely to find and track all of the partials.
12pt (3) A good equalization for noise-reduction applications is to ``flatten'' the noise floor. This option is useful when it is desired to set a fixed (frequency-independent) track rejection threshold just above the noise level.
12pt (4) A fourth option is to perform adaptive equalization of types (2) or (3) above. That is, equalize each spectrum independently, or compute the equalization as a function of a weighted average of the most recent power spectrum (FFT squared magnitude) estimates.
Apart from equalization, another preprocessing strategy which has proven very useful is to reverse the sound in time. The attack of most sounds is quite ``noisy'' and PARSHL has a hard time finding the relevant partials in such a complex spectrum. Once the sound is reversed the program will encounter the end of the sound first, and since in most instrumental sounds this is a very stable part, the program will find a very clear definition of the partials. When the program gets to the sound attack, it will already be tracking the main partials. Since PARSHL has a fixed number of oscillators which can be allocated to discovered tracks, and since each track which disappears removes its associated oscillator from the scene forever,H.3 analyzing the sound tail to head tends to allocate the oscillators to the most important frequency tracks first.
The simplest application of PARSHL is as an analysis tool since we can get a very good picture of the evolution of the sound in time by looking at the amplitude, frequency and phase trajectories. The tracking characteristics of the technique yield more accurate amplitudes and frequencies than if the analysis were done with an equally spaced bank of filters (the traditional STFT implementation).
In speech applications, the most common use of the STFT is for data-reduction. With a set of amplitude, frequency and phase functions we can get a very accurate resynthesis of many sounds with much less information than for the original sampled sounds. From our work it is still not clear how important is the phase information in the case of resynthesis without modifications, but McAulay and Quatieri  have shown the importance of phase in the case of speech resynthesis.
Some of the most interesting musical applications of the STFT techniques are given by their ability to separate temporal from spectral information, and, within each spectrum, pitch and harmonicity from formant information. In §H.0.5, Parameter Modifications, we discussed some of them, such as time scaling and pitch transposition. But this group of applications has a lot of possibilities that still need to be carefully explored. From the few experiments we have done to date, the tools presented give good results in situations where less flexible implementations do not, namely, when the input sound has inharmonic spectra and/or rapid frequency changes.
The main characteristic that differentiates this model from the traditional ones is the selectivity of spectral information and the phase tracking. This opens up new applications that are worth our attention. One of them is the use of additive synthesis in conjunction with other synthesis techniques. Since the program allows tracking of specific spectral components of a sound, we have the flexibility of synthesizing only part of a sound with additive, synthesis, leaving the rest for some other technique. For example, Serra  has used this program in conjunction with LPC techniques to model bar percussion instruments, and Marks and Polito  have modeled piano tones by using it in conjunction with FM synthesis . David Jaffe has had good success with birdsong, and Rachel Boughton used PARSHL to create abstractions of ocean sounds.
One of the problems encountered when using several techniques to synthesize the same sound is the difficulty of creating the perceptual fusion of the two synthesis components. By using phase information we have the possibility of matching the phases of the additive synthesis part to the rest of the sound (independently of what technique was used to generate it). This provides improved signal ``splicing'' capability, allowing very fast cross-fades (e.g., over one frame period).
PARSHL was originally written to properly analyze the steady state of piano sounds; it did not address modeling the attack of the piano sound for purposes of resynthesis. The phase tracking was primarily motivated by the idea of splicing the real attack (sampled waveform) to its synthesized steady state. It is well known that additive synthesis techniques have a very hard time synthesizing attacks, both due to their fast transition and their ``noisy'' characteristics. The problem is made more difficult by the fact that we are very sensitive to the quality of a sound's attack. For plucked or struck strings, if we are able to splice two or three periods, or a few milliseconds, of the original sound into our synthesized version the quality can improve considerably, retaining a large data-reduction factor and the possibility of manipulating the synthesis part. When this is attempted without the phase information, the splice, even if we do a smooth cross-fade over a number of samples, can be very noticeable. By simply adding the phase data the task becomes comparatively easy, and the splice is much closer to inaudible.
In this appendix, an analysis/synthesis technique based on a sinusoidal representation was presented that has proven to be very appropriate for signals which are well characterized as a sum of inharmonic sinusoids with slowly varying amplitudes and frequencies. The previously used harmonic vocoder techniques have been relatively unwieldy in the inharmonic case, and less robust even in the harmonic case. PARSHL obtains the sinusoidal representation of the input sound by tracking the amplitude, frequency, and phase of the most prominent peaks in a series of spectra computed using a Cooley-Tukey Fast Fourier Transform (FFT) of successive, overlapping, windowed data frames, taken over the duration of a sound. We have mentioned some of the musical applications of this sinusoidal representation.
Continuing the work with this analysis/synthesis technique we are implementing PARSHL on a Lisp Machine with an attached FPS AP120B array processor. We plan to study further its sound transformation possibilities and the use of PARSHL in conjunction with other analysis/synthesis techniques such as Linear Predictive Coding (LPC) .
The basic ``FFT processor'' at the heart of PARSHL provides a ready point of departure for many other STFT applications such as FIR filtering, speech coding, noise reduction, adaptive equalization, cross-synthesis, and many more. The basic parameter trade-offs discussed in this appendix are universal across all of these applications.
Although PARSHL was designed to analyze piano recordings, it has proven very successful in extracting additive synthesis parameters for radically inharmonic sounds. It provides interesting effects when made to extract peak trajectories in signals which are not describable as sums of sinusoids (such as noise or ocean recordings). PARSHL has even demonstrated that speech can be intelligible after reducing it to only the three strongest sinusoidal components.
The surprising success of additive synthesis from spectral peaks suggests a close connection with audio perception. Perhaps timbre perception is based on data reduction in the brain similar to that carried out by PARSHL. This data reduction goes beyond what is provided by critical-band masking. Perhaps a higher-level theory of ``timbral masking'' or ``main feature dominance'' is appropriate, wherein the principal spectral features serve to define the timbre, masking lower-level (though unmasked) structure. The lower-level features would have to be restricted to qualitatively similar behavior in order that they be ``implied'' by the louder features. Another point of view is that the spectral peaks are analogous to the outlines of figures in a picture--they capture enough of the perceptual cues to trigger the proper percept; memory itself may then serve to fill in the implied spectral features (at least for a time).
Techniques such as PARSHL provide a powerful analysis tool toward extracting signal parameters matched to the characteristics of hearing. Such an approach is perhaps the best single way to obtain cost-effective, analysis-based synthesis of any sound.
The authors of  thank Dynacord, Inc., for supporting the development of the first version of PARSHL in the summer of 1985. We also wish to acknowledge the valuable contributions of Gerold Schrutz (of Dynacord) during that time.
The software listing below is in the SAIL programming language (generally a superset of ALGOL). Since procedures are defined before they are used, the listing starts out defining basic utilities, progressing to higher levels until finally the top level is reached. As a result, it is usually easier start read the top level procedure at the end first, and then work backwards to fill in the details.
The SAIL keyboard had various non-standard characters which are spelled out here using TeX equivalents such as α#alpha; and β#beta;.
IF ln>1 THEN RootName  <-  Gname[1 to 6-lc-1]&CodeString&"2"
[n>\alpha-T - FFT length (must be a power of 2).
[n>\alpha-D - Number of samples of input signal per FFT frame.
[n>\alpha-H - Number of samples of input signal to advance between FFT's.
[n>\alpha-L - Length of filter impulse response (if known).
[s>\alpha-I - Input sound file.
[s>\alpha-O - Output sound file.
[s>\alpha-F - Input filter file.
ALT - Exit to Outer level.
[n]\alpha-B - Buffer display code. If negative, all time buffers are displayed.
and return the X-value where the extremum is attained.
of zero slope in the parabola through the three points.
is clipped to lie at either 1 or -1 as appropriate.
Hyst = Wiggles less than Hyst in magnitude are ignored.
MinWidth = Minimum peak width in indices, after blanking.
Narrower peaks are removed and ignored.
BlankWidth = Minimum blanking interval in indeces.
for efficiency reasons (would rather measure width first).
i1,i2 = index boundaries for the search within X.
The return value is the number of peaks actually found.
COMMENT Find amplitudes (dB) and frequencies (Hz) of all partials in XmagDB.
Npartials = the maximum number of partials to find.
It is set to the actual number of partials found on return.
MinWid = minimum acceptable peak width in FFT bins.
Fc1,Fc2 = lower and upper frequency bounds in Hz.
No partials will be allowed outside this interval.
COMMENT Return next active oscillator after CurOsc, with wrap-around.
COMMENT Return next free oscillator after CurOsc, with wrap-around.
COMMENT Return next Ending oscillator after CurOsc, with wrap-around.
COMMENT Return free oscillator with frequency closest to NewFrq.
# Search for a line within specs, starting from where last one was.
then running because LinOfOsc[CurOsc] will then be positive.
COMMENT UpdateMap - Assign oscillators target values to partials.
the problem of partials appearing and disappearing.
This version of UpdateMap assumes lines to be sorted by ascending frequency.
Initialization is trivial, so assume we are into the analysis at time Frame.
its line among those not already taken.
assigned oscs than than lines because of the "taken" mark interlock.
However, there can be lines left over after all bands have been searched.
array, and an oscillator is dispatched onto each line found not to be taken.
An oscillator marks a line as taken by storing its id in an array.
can be given the line. In the current implementation, only a warning is issued.
to 0. A hop is typically on the order of two periods of sound.
unintelligible. Thus, UpDateMap is based on these changes.
DAJ mentions what if a line is crossing back and forth between two bands?
captures the other lines osc.
OSC 1 claims LINE K+1 instead of LINE K which it normally claims.
the bumped osc should get another pass to look for a "consolation line".
one oscillator turns off and another will hopefully start up elsewhere.
spectrum is searched for a local max nearest the current osc frq.
a "virtual line" with its own AMP and FRQ.
over the first active oscillators in the loop to MaxOscs below.
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