Analog electrical elements such as mixers, filters, transfer oscillators, isolating buffers, dividers, and even transmission lines contribute technical noise and unwanted environmental coupling in time and frequency measurements. Software defined radio (SDR) techniques replace many of these analog components with digital signal processing (DSP) on rapidly sampled signals. We demonstrate that, generically, commercially available multi-channel SDRs are capable of time and frequency metrology, outperforming purpose-built devices by as much as an order-of-magnitude. For example, for signals at 10 MHz and 6 GHz, we observe SDR time deviation noise floors of about 20 fs and 1 fs, respectively, in under 10 ms of averaging. Examining the other complex signal component, we find a relative amplitude measurement instability of 3e-7 at 5 MHz. We discuss the scalability of a SDR-based system for simultaneous measurement of many clocks. SDR's frequency agility allows for comparison of oscillators at widely different frequencies. We demonstrate a novel and extreme example with optical clock frequencies differing by many terahertz: using a femtosecond-laser frequency comb and SDR, we show femtosecond-level time comparisons of ultra-stable lasers with zero measurement dead-time.
Some limitations in DMTD can be addressed by replacing certain analog processing steps with digital implementations. The TIC can be dramatically redesigned @cite_18 with much higher effective @math . One group @cite_14 replaced the TIC by digitizing the mixed and filtered signals at @math and later eliminated the mixers with high-speed direct sampling of the input signals @cite_8 . Others have replaced mixer-based spectral down-conversion with aliasing through under-sampling @cite_40 . Early consideration of a direct-sampling system @cite_0 very similar to the present work showed plausible limits due to quantization effects alone can be @math for averaging intervals @math . While high-speed samples can be processed entirely in software @cite_46 or with custom hardware @cite_2 , this work explores oscillator metrology using an inexpensive, commercially available, unmodified software defined radio (SDR). We note a similar approach for characterizing ADCs @cite_45 . We employ an ADC noise cancelation technique in the time domain, which perhaps is analogous to cross-spectral analysis @cite_48 in the frequency domain.
@cite_18 @cite_14 @cite_8 @cite_48 @cite_0 @cite_40 @cite_45 @cite_2 @cite_46
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As communication systems scale up in speed and bandwidth, the cost and power consumption of high-precision (e.g., 8-12 bits) analog-to-digital conversion (ADC) becomes the limiting factor in modern transceiver architectures based on digital signal processing. In this work, we explore the impact of lowering the precision of the ADC on the performance of the communication link. Specifically, we evaluate the communication limits imposed by low-precision ADC (e.g., 1-3 bits) for transmission over the real discrete-time additive white Gaussian noise (AWGN) channel, under an average power constraint on the input. For an ADC with K quantization bins (i.e., a precision of log2 K bits), we show that the input distribution need not have any more than K+1 mass points to achieve the channel capacity. For 2-bin (1-bit) symmetric quantization, this result is tightened to show that binary antipodal signaling is optimum for any signal-to- noise ratio (SNR). For multi-bit quantization, a dual formulation of the channel capacity problem is used to obtain tight upper bounds on the capacity. The cutting-plane algorithm is employed to compute the capacity numerically, and the results obtained are used to make the following encouraging observations : (a) up to a moderately high SNR of 20 dB, 2-3 bit quantization results in only 10-20 reduction of spectral efficiency compared to unquantized observations, (b) standard equiprobable pulse amplitude modulated input with quantizer thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high SNR, and works well at low to moderate SNRs as well. Wideband analog signals push contemporary analog-to-digital conversion (ADC) systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the band limit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its band limit in hertz. Simulations suggest that the random demodulator requires just O(K log(W K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W hertz. In contrast to Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system's performance that supports the empirical observations. Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters. Distributed sampling and reconstruction of a physical field using an array of sensors is a problem of considerable interest in environmental monitoring applications of sensor networks. Our recent work has focused on the sampling of bandlimited sensor fields. However, sensor fields are not perfectly bandlimited but typically have rapidly decaying spectra. In a classical sampling set-up it is possible to precede the A D sampling operation with an appropriate analog anti-aliasing filter. However, in the case of sensor networks, this is infeasible since sampling must precede filtering. We show that even though the effects of aliasing on the reconstruction cannot be prevented due to the "filter-less" sampling constraint, they can be suitably controlled by oversampling and carefully reconstructing the field from the samples. We show using a dither-based scheme that it is possible to estimate non-bandlimited fields with a precision that depends on how fast the spectral content of the field decays. We develop a framework for analyzing non-bandlimited fields that lead to upper bounds on the maximum pointwise error for a spatial bit rate of R bits meter. We present results for fields with exponentially decaying spectra as an illustration. In particular, we show that for fields f(t) with exponential tails; i.e., F( spl omega ) < spl pi spl alpha sup - spl alpha | spl omega | , the maximum pointwise error decays as c2e sup -a sub 1 spl radic R+ c3 1 spl radic R (e sup -2a sub 1 spl radic R) with spatial bit rate R bits meter. Finally, we show that for fields with spectra that have a finite second moment, the distortion decreases as O((1 N) sup 2 3 ) as the density of sensors, N, scales up to infinity . We show that if D is the targeted non-zero distortion, then the required (finite) rate R scales as O (1 spl radic D log 1 D). The patient dose in computed tomography (CT) imaging is linked to measurement noise. Various noise-reduction techniques have been developed that adapt structure preserving filters like anisotropic diffusion or bilateral filters to CT noise properties. We introduce a structure adaptive sinogram (SAS) filter that incorporates the specific properties of the CT measurement process. It uses a point-based forward projector to generate a local structure representation called ray contribution mask (RCM). The similarities between neighboring RCMs are used in an enhanced variant of the bilateral filtering concept, where the photometric similarity is replaced with the structural similarity. We evaluate the performance in four different scenarios: The robustness against reconstruction artifacts is demonstrated by a scan of a high-resolution-phantom. Without changing the modulation transfer function (MTF) nor introducing artifacts, the SAS filter reduces the noise level by 13.6 . The image sharpness and noise reduction capabilities are visually assessed on in vivo patient scans and quantitatively evaluated on a simulated phantom. Unlike a standard bilateral filter, the SAS filter preserves edge information and high-frequency components of organ textures well. It shows a homogeneous noise reduction behavior throughout the whole frequency range. The last scenario uses a simulated edge phantom to estimate the filter MTF for various contrasts: the noise reduction for the simple edge phantom exceeds 80 . For low contrasts at 55 Hounsfield units (HU), the mid-frequency range is slightly attenuated, at higher contrasts of approximately 100 HU and above, the MTF is fully preserved. We propose a novel measurement system that evaluates the frequency stability of high-precision oscillators such as atomic oscillators. This measurement system consists of a pair of high-speed analog-to-digital converters (ADCs) and digital-signal-processing (DSP) circuits on a field programmable gate array. The pair of high-speed ADCs simultaneously digitizes the two sinusoidal-voltage outputs from the oscillator under test and a reference oscillator. The DSP circuits calculate the phase difference between the two sinusoidal voltages. The frequency stability evaluated as the Allan deviation sigmay(tau) is calculated from the phase difference. The main advantage of this system is that the hardware configuration is much more compact than the conventional systems using a dual mixer and a local oscillator. Nonetheless, the system noise floor of the prototype at the nominal frequency of 5 MHz is sigmay(1000 s) = 6.8 times 10-17, which is sufficient to evaluate a commercial hydrogen maser oscillator and is better by a factor of 5 than our previously reported system. We have verified that the measurement accuracy of the prototype depends on the nominal frequency and the level of the sinusoidal voltages, but it does not depend on the initial phase difference and offset frequency. Abstract : The Naval Research Laboratory (NRL) is developing a digital phase measurement system. The measurement system uses high speed Analog to Digital Converters (ADC) to make tens of millions of measurements per second, Digital Signal Processing (DSP) hardware for intermediate calculations, and a PC for the final phase calculations. Performance of the present configuration is limited by a 12-bit analog-to-digital converter. Averaging times can be as small as 0.0001 seconds. Multiple input frequencies to over 10 MHz can be measured simultaneously. Modular construction will allow for expansion to many channels. Absolute phase measurements are possible. Inputs to channels can be switched between frequencies and then returned to an original frequency without losing phase coherency of the measurements. This system to be used in the laboratory and may be used on the GPS satellites to monitor a hot backup clock. The basic system measures the coefficient of a Discrete Fourier Transform (DFT) at the assumed frequency of the input signal. This paper will describe the special purpose DSP hardware and software used to measure the signal and transform the measurements into conventional clock parameters. This paper proposes an end-to-end approach for single-channel speaker-independent multi-speaker speech separation, where time-frequency (T-F) masking, the short-time Fourier transform (STFT), and its inverse are represented as layers within a deep network. Previous approaches, rather than computing a loss on the reconstructed signal, used a surrogate loss based on the target STFT magnitudes. This ignores reconstruction error introduced by phase inconsistency. In our approach, the loss function is directly defined on the reconstructed signals, which are optimized for best separation. In addition, we train through unfolded iterations of a phase reconstruction algorithm, represented as a series of STFT and inverse STFT layers. While mask values are typically limited to lie between zero and one for approaches using the mixture phase for reconstruction, this limitation is less relevant if the estimated magnitudes are to be used together with phase reconstruction. We thus propose several novel activation functions for the output layer of the T-F masking, to allow mask values beyond one. On the publicly-available wsj0-2mix dataset, our approach achieves state-of-the-art 12.6 dB scale-invariant signal-to-distortion ratio (SI-SDR) and 13.1 dB SDR, revealing new possibilities for deep learning based phase reconstruction and representing a fundamental progress towards solving the notoriously-hard cocktail party problem. A time domain blind source separation algorithm of convolutive sound mixtures is studied based on a compact partial inversion formula in closed form. An l1-constrained minimization problem is formulated to find demixing filter coefficients for source separation while capturing scaling invariance and sparseness of solutions. The minimization aims to reduce (lagged) cross correlations of the mixture signals which are modeled stochastically. The problem is non-convex, however it is put in a nonlinear least square form where the robust and convergent Levenberg-Marquardt iterative method is applicable to compute local minimizers. Efficiency is achieved in recovering lower dimensional demixing filter solutions than the physical ones. Computations on recorded and synthetic mixtures show satisfactory performance, and are compared with other iterative methods. The problem of sampling signals that are not admissible within the classical Shannon framework has received much attention in the recent past. Typically, these signals have a parametric representation with a finite number of degrees of freedom per time unit. It was shown that, by choosing suitable sampling kernels, the parameters can be computed by employing high-resolution spectral estimation techniques. In this letter, we propose a simple acquisition and reconstruction method within the framework of multichannel sampling. In the proposed approach, an infinite stream of nonuniformly-spaced Dirac impulses can be sampled and accurately reconstructed provided that there is at most one Dirac impulse per sampling period. The reconstruction algorithm has a low computational complexity, and the parameters are computed on the fly. The processing delay is minimal just the sampling period. We propose sampling circuits using inexpensive passive devices such as resistors and capacitors. We also show how the approach can be extended to sample piecewise-constant signals with a minimal change in the system configuration. We provide some simulation results to confirm the theoretical findings. A skip and fill algorithm is developed to digitally self-calibrate pipelined analog-to-digital converters (ADC's) in real time. The proposed digital calibration technique is applicable to capacitor-ratioed multiplying digital-to-analog converters (MDACs) commonly used in multistep or pipelined ADCs. This background calibration process can replace, in effect, a trimming procedure usually done in the factory with a hidden electronic calibration. Unlike other self-calibration techniques working in the foreground, the proposed technique is based on the concept of skipping conversion cycles randomly but filling in data later by nonlinear interpolation. This opens up the feasibility of digitally implementing calibration hardware and simplifying the task of self-calibrating multistep or pipelined ADCs. The proposed method improves the performance of the inherently fast ADCs by maintaining simple system architectures. To measure errors resulting from capacitor mismatch, of amp DC gain, offset, and switch feedthrough in real time, the calibration test signal is injected in place of the input signal using a split-reference injection technique. Ultimately, the missing signal within two-thirds of the Nyquist bandwidth is recovered with 16-b accuracy using a forty-fourth order polynomial interpolation, behaving essentially as an FIR filter,. It is well known that at low-bit-rate block discrete cosine transform compressed image exhibits visually annoying blocking and ringing artifacts. In this paper, we propose a noniterative, wavelet-based deblocking algorithm to reduce both types of artifacts. The algorithm exploits the fact that block discontinuities are constrained by the dc quantization interval of the quantization table, as well as the behavior of wavelet modulus maxima evolution across wavelet scales to derive appropriate threshold maps at different wavelet scales. Since ringing artifacts occur near strong edges, which can be located either along block boundaries or within blocks, suppression of block discontinuities does not always reduce ringing artifacts. By exploiting the behavior of ringing artifacts in the wavelet domain, we propose a simple yet effective method for the suppression of such artifacts. The proposed algorithm can suppress both block discontinuities and ringing artifacts effectively while preserving true edges and textural information. Simulation results and extensive comparative study with both iterative and noniterative methods reported in the literature have shown the effectiveness of our algorithm. Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. We consider inference in a general data-driven object-based model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. We work in the short-time Fourier transform (STFT) domain, where convolution is routinely approximated as linear instantaneous mixing in each frequency band. Each source STFT is given a model inspired from nonnegative matrix factorization (NMF) with the Itakura-Saito divergence, which underlies a statistical model of superimposed Gaussian components. We address estimation of the mixing and source parameters using two methods. The first one consists of maximizing the exact joint likelihood of the multichannel data using an expectation-maximization (EM) algorithm. The second method consists of maximizing the sum of individual likelihoods of all channels using a multiplicative update algorithm inspired from NMF methodology. Our decomposition algorithms are applied to stereo audio source separation in various settings, covering blind and supervised separation, music and speech sources, synthetic instantaneous and convolutive mixtures, as well as professionally produced music recordings. Our EM method produces competitive results with respect to state-of-the-art as illustrated on two tasks from the international Signal Separation Evaluation Campaign (SiSEC 2008). We study the problem of optimal sub-Nyquist sampling for perfect reconstruction of multiband signals. The signals are assumed to have a known spectral support spl Fscr that does not tile under translation. Such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching Landau's (1967) lower bound equal to the measure of spl Fscr . For signals with sparse spl Fscr , this rate can be much smaller than the Nyquist rate. Unfortunately the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In a previous study, we derived bounds on the error due to mismodeling and sample additive noise. Adopting these bounds as performance measures, we consider the problems of optimizing the reconstruction sections of the system, choosing the optimal base sampling rate, and designing the nonuniform sampling pattern. We find that optimizing these parameters can improve system performance significantly. Furthermore, uniform sampling is optimal for signals with spl Fscr that tiles under translation. For signals with nontiling spl Fscr , which are not amenable to efficient uniform sampling, the results reveal increased error sensitivities with sub-Nyquist sampling. However, these can be controlled by optimal design, demonstrating the potential for practical multifold reductions in sampling rate. We address the problem of estimating spectral lines from irregularly sampled data within the framework of sparse representations. Spectral analysis is formulated as a linear inverse problem, which is solved by minimizing an l1-norm penalized cost function. This approach can be viewed as a basis pursuit de-noising (BPDN) problem using a dictionary of cisoids with high frequency resolution. In the studied case, however, usual BPDN characterizations of uniqueness and sparsity do not apply. This paper deals with the l1-norm penalization of complex-valued variables, that brings satisfactory prior modeling for the estimation of spectral lines. An analytical characterization of the minimizer of the criterion is given and geometrical properties are derived about the uniqueness and the sparsity of the solution. An efficient optimization strategy is proposed. Convergence properties of the iterative coordinate descent (ICD) and iterative reweighted least-squares (IRLS) algorithms are first examined. Then, both strategies are merged in a convergent procedure, that takes advantage of the specificities of ICD and IRLS, considerably improving the convergence speed. The computation of the resulting spectrum estimator can be implemented efficiently for any sampling scheme. Algorithm performance and estimation quality are illustrated throughout the paper using an artificial data set, typical of some astrophysical problems, where sampling irregularities are caused by day night alternation. We show that accurate frequency location is achieved with high resolution. In particular, compared with sequential Matching Pursuit methods, the proposed approach is shown to achieve more robustness regarding sampling artifacts. A 100 MS s pipelined ADC is digitally calibrated by a slow SigmaDelta ADC using a least-mean-square (LMS) algorithm. Both linear and nonlinear memoryless residue gain errors of the pipeline stages are adaptively corrected. With a 411 kHz sinusoidal input, the peak SNDR improves from 28 dB to 59 dB and the SFDR improves from 29 dB to 68 dB. The complete 0.13 mu ADC SoC occupies a die size of 3.7 mm times 4.7 mm, and consumes a total power of 448 mW. We investigate the uplink throughput achievable by a multiple-user (MU) massive multiple-input multiple-output (MIMO) system, in which the base station is equipped with a large number of low-resolution analog-to-digital converters (ADCs). Our focus is on the case where neither the transmitter nor the receiver have any a priori channel state information. This implies that the fading realizations have to be learned through pilot transmission followed by channel estimation at the receiver, based on coarsely quantized observations. We propose a novel channel estimator, based on Bussgang’s decomposition, and a novel approximation to the rate achievable with finite-resolution ADCs, both for the case of finite-cardinality constellations and of Gaussian inputs, that is accurate for a broad range of system parameters. Through numerical results, we illustrate that, for the 1-bit quantized case, pilot-based channel estimation together with maximal-ratio combing, or zero-forcing detection enables reliable multi-user communication with high-order constellations, in spite of the severe nonlinearity introduced by the ADCs. Furthermore, we show that the rate achievable in the infinite-resolution (no quantization) case can be approached using ADCs with only a few bits of resolution. We finally investigate the robustness of low-ADC-resolution MU-MIMO uplink against receive power imbalances between the different users, caused for example by imperfect power control. Standard Mel frequency cepstrum coefficient (MFCC) computation technique utilizes discrete cosine transform (DCT) for decorrelating log energies of filter bank output. The use of DCT is reasonable here as the covariance matrix of Mel filter bank log energy (MFLE) can be compared with that of highly correlated Markov-I process. This full-band based MFCC computation technique where each of the filter bank output has contribution to all coefficients, has two main disadvantages. First, the covariance matrix of the log energies does not exactly follow Markov-I property. Second, full-band based MFCC feature gets severely degraded when speech signal is corrupted with narrow-band channel noise, though few filter bank outputs may remain unaffected. In this work, we have studied a class of linear transformation techniques based on block wise transformation of MFLE which effectively decorrelate the filter bank log energies and also capture speech information in an efficient manner. A thorough study has been carried out on the block based transformation approach by investigating a new partitioning technique that highlights associated advantages. This article also reports a novel feature extraction scheme which captures complementary information to wide band information; that otherwise remains undetected by standard MFCC and proposed block transform (BT) techniques. The proposed features are evaluated on NIST SRE databases using Gaussian mixture model-universal background model (GMM-UBM) based speaker recognition system. We have obtained significant performance improvement over baseline features for both matched and mismatched condition, also for standard and narrow-band noises. The proposed method achieves significant performance improvement in presence of narrow-band noise when clubbed with missing feature theory based score computation scheme. A major obstacle for widespread deployment of frequency division duplex (FDD)-based Massive multiple-input multiple-output (MIMO) communications is the large signaling overhead for reporting full downlink (DL) channel state information (CSI) back to the basestation (BS), in order to enable closed-loop precoding. We completely remove this overhead by a deep-learning based channel extrapolation (or "prediction") approach and demonstrate that a neural network (NN) at the BS can infer the DL CSI centered around a frequency @math by solely observing uplink (UL) CSI on a different, yet adjacent frequency band around @math ; no more pilot reporting overhead is needed than with a genuine time division duplex (TDD)-based system. The rationale is that scatterers and the large-scale propagation environment are sufficiently similar to allow a NN to learn about the physical connections and constraints between two neighboring frequency bands, and thus provide a well-operating system even when classic extrapolation methods, like the Wiener filter (used as a baseline for comparison throughout) fails. We study its performance for various state-of-the-art Massive MIMO channel models, and, even more so, evaluate the scheme using actual Massive MIMO channel measurements, rendering it to be practically feasible at negligible loss in spectral efficiency when compared to a genuine TDD-based system.