the following detailed description describes the invention with reference to an illustrative embodiment in which the carrier frequency is 2 ghz . the frequency of 2 ghz has been chosen only for discussion purposes ; the carrier frequency can be any frequency suitable for rf transmission . still further , if the invention is to be employed for modulating a waveform for transmission other than electromagnetic propagation through the medium of air , such as transmission of extremely low frequency ( elf ) signals through a solid medium , then the carrier frequency could be any suitable frequency for the transmission medium and method to be employed . fig1 shows the result of commutating a typical baseband signal with a (− 1 ) n waveform at a clock rate of 4 ghz . the output spectrum is now centered around 2 ghz with a low noise floor in the neighborhood of the carrier frequency . although obscured by the resolution of the plot , there are two separate sidebands , which is the expected result of double sideband suppressed - carrier modulation . the basic operation of a delta - sigma transmitter has been described in u . s . patent application ser . no . 10 / 998 , 212 , published as publication number us 2005 / tbd and entitled direction conversion delta - sigma transmitter , which is incorporated herein by reference in its entirety . that transmitter takes advantage of the fact that commutation has the effect of upconverting a baseband signal to a higher frequency as shown in fig1 , with two separate sidebands . the commutation also introduces unwanted quantization or commutation noise that should be filtered out before transmission . for purposes of describing the present invention , the basic structure of a delta - sigma transmitter is shown in fig2 a or 2 b . quadrature inputs i and q are n - bit representations of the real and imaginary parts of the baseband waveform . those two n - bit signals are input to delta - sigma modulators 11 and 12 . delta - sigma modulators 11 and 12 each produce signals which are pulse width modulated ( pwm ) signals whose pulse widths represent the values of the n - bit input signals . both the n - bit inputs and the pwm outputs from the delta - sigma modulators carry the information to be transmitted , though in different forms , and therefore constitute information signals . the pwm information signals are the inputs to commutators 13 and 14 . each commutator is a switch that implements the switching or gating function (− 1 ) n , i . e ., multiplying the signal by + 1 and − 1 . alternatively , the commutators could implement a simple on or off gating of the modulator output , because the hi and lo voltage values of the pmw signal are not important . either way , the commutator produces a gated version of the pwm information signal . in a broad sense , the transmitter circuit includes an information circuit for producing an information signal , and a commutator circuit for commutating the information signal thereby producing an upconverted version of the information signal at a transmission frequency , such as a radio frequency carrier frequency , plus the unwanted quantization noise introduced by the conversion . the two commutators 13 and 14 are respectively clocked by clock signals that are at the same commutator clock frequency - but 90 degrees out of phase , and produced by quadrature clock generator block 16 . that is , the two clock signals are in quadrature . the commutated information signals produced by the commutator are input to either a combining fir filter 18 that combines the i and q components to produce a single output as shown in fig2 a , or to a complex fir filter 18 ′ that performs complex filtering and produces quadrature outputs as shown in fig2 b . either way , the output digital filter produces a filtered modulated signal . as shown in the figures , the same clock frequency is used to clock both the commutators and the digital filter . as used herein , the clocks for both the commutators and for the digital filter may be referred to as the “ same ” clock , or that the clocks operate at the “ same ” or “ substantially the same ” frequency . that terminology will be understood to encompass any method of generating two clocks signals , whether produced from a common clock source and individually buffered and therefore physically separated or not , or even two different clocks that operate at respective frequencies that are slightly different but yet close enough together such that the advantage is realized of a self - tuning output filter whose frequency response automatically changes to tracks changes in the carrier frequency as the commutator clock frequency is varied . under such conditions the passband of the digital filter will continue to stay centered around approximately the carrier frequency , i . e ., approximately one half the commutator clock frequency , thus enabling the digital filter to sufficiently attenuate the quantization noise introduced by the commutator in order to achieve acceptable performance as demanded by a particular application . what is important is that the commutator is clocked so that the modulated information signal has a given carrier frequency , and the digital filter is clocked so that it filters out noise that is substantially out of the range of the carrier frequency plus or minus the baseband information frequency and any sidelobes associated therewith depending on the modulation method used . for example , if the modulation scheme used is amplitude modulation , the bandwidth of interest is plus or minus the baseband information frequency ; if frequency modulation is used , the bandwidth of interest will be wider . in the preferred embodiment , for simplicity the commutator clock and the digital filter are derived from the same ultimate clock source , with a 90 degree phase shift introduced for the quadrature clock , with both the commutator and the digital filter being clocked at twice the carrier frequency . methods of generating a variable clock signal , i . e ., a clock signal whose frequency is variable , so that the carrier frequency of the transmitter can be changed to effect a new carrier frequency of the filtered modulated signal , are well known in the art . the basic design of the output digital filter is simplified by the fact that output samples of the delta - sigma transmitter are presented either in single - bit format ( i . e ., one bit each for i and q ) or thermometric code ( i . e ., where an n - bit output is conveyed using 2 n − 1 thermometric bits such that a number m is represented with digits 1 through m equal to logic “ 1 ” and all higher digits equal to logic “ 0 ”). under these circumstances , if flip - flops with both q and q outputs available are used , both positive and negative fir coefficients can be implemented using either voltage or current as the operating state - variable . fig3 and 4 summarize the operation of the present invention according to simulations performed . in the preferred embodiment the digital output filter operates at a filter clock rate that is twice the desired carrier frequency . in the illustrative embodiment , the carrier frequency is 2 ghz so the clock frequency is 4 ghz . fig3 a illustrates the passband characteristic of a fir high pass filter designed with a clock rate of 4 ghz . since the filter is a discrete time filter , the passband characteristic is mirrored around half the sample rate , or 2 ghz . alternatively , the digital filter could be a passband digital filter that is clocked at a different integer multiple of the carrier frequency . fig3 b illustrates operation of the filter upon the double sideband suppressed carrier output shown in fig1 . that is , fig3 b shows the spectrum of fig1 after having been filtered by the filter of fig3 a . as can be seen , the filtered spectrum falls off rapidly and becomes nearly zero outside the band of approximately 2 . 0 ghz ± 0 . 1 ghz . outside of that band the quantization noise is suppressed leaving essentially only the desired double sideband signal , i . e ., the baseband signal modulated up to the carrier frequency . fig4 is an expanded view of the center region of fig3 b showing in greater detail the output spectrum in the region of the carrier frequency . fig5 illustrates a representative implementation 18 of the digital filter of the present invention that uses voltage as the state variable , and illustrating a single ( i or q ) output from the commutator . the raw commutated delta - sigma modulator output , which is essentially a pulse code modulated ( pcm ) sequence clocking at twice the carrier frequency , is fed into a serial shift register constructed from a chain of d flip - flops 30 ( 1 ) . . . 30 ( n ). the flip - flops form the delay elements within the fir filter . the coefficients are realized by resistive summing . positive impulse response coefficients are implemented by connecting the “ q resistors ” 32 , 34 , . . . 40 of the corresponding stage to the positive output pin and the “ q resistors ” 33 , 35 , . . . 41 to the negative output pin . the resistors form part of a resistive summing network , with the different resistor values constituting different tap weights and feeding into the summing node , such that differently weighted versions of the respective digital storage element outputs or inputs are summed together to implement the filter . negative coefficients are implemented by swapping q and q . in the figure , the filter has positive coefficients for the 0 th , 2 nd , and ( n − 1 ) stages , and negative coefficients for the 1 st and n th stages . resistive summing networks are well known in the art . the transfer function of the output filter is given by the equation in z - transform notation : h ( z )= h 0 + h 1 z − 1 + h 2 z − 2 +. . . + h n z − n where the j th coefficient h j is given by the formula : h j = g j g 0 + g 1 + g 2 + … + g n , and ⁢ ⁢ g j ≡ r j - 1 where h 0 . . . h n are the fir filter tap coefficient values , and where r j is the value of the j th resistor . one possible procedure for determining the tap coefficient values is as follows . begin with the quantization noise spectrum that is created by generating the waveform , as shown in fig1 . we want to suppress the noise in order to keep it down to an acceptable level , as defined by the particular application . synthesize a low pass filter ( lpf ) using standard techniques for synthesizing fir filters that would result in the desired noise suppression , then substitute − z for z . standard techniques for synthesizing lpf tap coefficients are well known in the literature , and include windowing or the remez exchange algorithm . fir and fir digital filter design techniques are taught in , for example , alan oppenheim and ronald w . schafer , digital signal processing ( prentice - hall 1975 ) at pp . 195 – 271 , which is hereby incorporated by reference for its teachings of digital filter theory and design . once the filter coefficient values are determined , choose a value for the largest coefficient ( the largest conductance or the smallest resistance ) and choose the remaining values of resistance so that the ratios between the corresponding conductances and largest conductance are preserved . the diagram in fig5 shows the output configured as a differential output . alternatively , the positive and negative outputs may be used as a single - ended output carrying the positive and negative sense of the filtered output , respectively . fig6 illustrates the method for converting the structure shown in fig5 into a real finite impulse response filter operating on the sum of i and q , using voltage as the state variable . the addition is performed by the resistor network and therefore care must be taken to ensure that resistor values are matched between the i and q outputs . note , as well , that the filter may also be configured to operate on the difference between i and q simply by reversing the sense of each of the differential outputs of the “ q ” resistors . when this transformation is used in conjunction with the application of the hilbert transform to the “ i ” modulation input to form the “ q ” modulation input , the upper and lower sidebands may be generated individually ( by selecting the sum or difference of the i and q outputs ). the filter structure of fig6 is similar to that of the filter structure of fig5 , although in fig6 only the j th filter stage is shown for convenience . all four resistors shown are of the same value . in order to change the sign of the filter coefficient , the connections 52 and 54 to the rest of the summing network would be swapped . the fir filter can also be configured as a complex filter operating on the complex set of i and q samples . there are many ways this may be realized including the use of the hilbert transform as well as polyphase filters . in this case , the filter would take on a form similar to that shown in fig6 except that the i and q resistor values would no longer be identical or connected to the same corresponding stage in the shift register . instead , the values would be scaled according to the cross - coupling coefficients for each of the stages in accordance with the equation given above for the filter transfer function . fig7 illustrates an implementation 18 ″ of the filter of the present invention in which current is used as the state variable . the current variable approach is mathematically similar to the voltage variable approach , except that the coefficients computed in the transfer function equation are represented by currents instead of voltages . in this approach , the coefficients are implemented by using the current values for each of the differential pairs . the output in this case is a pair of “ open drain ” transistors 510 , 511 to which pull - up resistors or an lc coupling network may be used to drive subsequent stages of amplification . the drain terminals are swapped to implement positive and negative coefficients . in the figure , current sources 50 ( 1 ) and 50 ( 3 ) represent positive coefficients , and current sources 50 ( 2 ) and 50 ( n ) represent negative coefficients , because latched values in stages 1 and stage 3 couple the respective drain sources to the filter output positive terminal , and inverted latched values in stages 2 and n couple the respective drain sources to the filter output negative terminal . although field effect transistors ( fets ) are shown in the figure , this embodiment may also be implemented using bipolar transistors . the current variable approach has two advantages over the voltage variable approach that make it a generally preferred choice for implementation in high - speed circuits : ( 1 ) the coefficients can be reprogrammed simply by changing the currents which is easier to do than switching in resistors to change coefficient values , and ( 2 ) the current approach can be arranged to have voltage gain so that the output may be driven directly into a load when appropriate . the circuit in fig7 may also be applied to the sum of , or difference between , i and q as well as configured as a complex filter in fashions analogous to the voltage variable case . there are multiple possible ways to generate the tail currents that represent the coefficients ( i 0 to i n ). fig8 shows one simple way which may be used for fixed coefficient applications , i . e ., those in which the coefficients do not have to be reprogrammed . this implementation uses a globally defined reference voltage in conjunction with a current setting resistor to implement each individual coefficient . the circuit in fig8 may also be further developed to permit the reprogramming of the coefficients digitally . fig9 illustrates one software programmable implementation 50 ( 1 )′ that uses adjustable current sources to permit setting the coefficients with n - bit resolution . switch 91 is closed for “ on ” and switch 92 is closed for “ off .” the switches for the other bits operate in the same fashion . a circuit may be implemented with n - bit accuracy using either n binary weighted currents , or 2 n − 1 identical current paths with thermometric coding . if necessary , the polarity of each coefficient may be inverted as well , by using additional current steering transistors in similar fashion to current mode logic circuits . although fets are employed here , this embodiment may also be implemented using bipolar transistors it will be appreciated that the term “ present invention ” as used herein should not be construed to mean that only a single invention having a single essential element or group of elements is presented . similarly , it will also be appreciated that the term “ present invention ” encompasses a number of separate innovations which can each be considered separate inventions . although the present invention has thus been described in detail with regard to the preferred embodiments and drawings thereof , it should be apparent to those skilled in the art that various adaptations and modifications of the present invention may be accomplished without departing from the spirit and the scope of the invention . as one example , although it is preferred that the output digital filter be an fir filter , the filter could be an infinite impulse response filter . additional ways could also used to realize analog coefficients as will be apparent to those skilled in the art . furthermore , although it is preferred , it is not strictly necessary that the digital filter produce an analog output directly ; rather then digital filter could be a filter having both a digital input and a digital output , with analog - to - digital conversion being performed on the digital output from the filter . accordingly , it is to be understood that the detailed description and the accompanying drawings as set forth hereinabove are not intended to limit the breadth of the present invention , which should be inferred only from the following claims and their appropriately construed legal equivalents .