Introduction to linear and nonlinear programming

An algorithm is presented for the estimation of the fundamental frequency (F0) of speech or musical sounds. It is based on the well-known autocorrelation method with a number of modifications that combine to prevent errors. The algorithm has several desirable features. Error rates are about three times lower than the best competing methods, as evaluated over a database of speech recorded together with a laryngograph signal. There is no upper limit on the frequency search range, so the algorithm is suited for high-pitched voices and music. The algorithm is relatively simple and may be implemented efficiently and with low latency, and it involves few parameters that must be tuned. It is based on a signal model (periodic signal) that may be extended in several ways to handle various forms of aperiodicity that occur in particular applications. Finally, interesting parallels may be drawn with models of auditory processing.

/pdf/yin-a-fundamental-frequency-estimator-for-speech-and-music-53voam3nec.pdf

YIN, a fundamental frequency estimator for speech and music

Quantization is a process that maps a continous or discrete set of values into approximations that belong to a smaller set. Quantization is a lossy: some information about the original data is lost in the process. The key to a successful quantization is therefore the selection of an error criterion – such as entropy and signal-to-noise ratio – and the development of optimal quantizers for this criterion.

Quantization

tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

Probability and Random Processes

A sinusoidal model for the speech waveform is used to develop a new analysis/synthesis technique that is characterized by the amplitudes, frequencies, and phases of the component sine waves. These parameters are estimated from the short-time Fourier transform using a simple peak-picking algorithm. Rapid changes in the highly resolved spectral components are tracked using the concept of "birth" and "death" of the underlying sine waves. For a given frequency track a cubic function is used to unwrap and interpolate the phase such that the phase track is maximally smooth. This phase function is applied to a sine-wave generator, which is amplitude modulated and added to the other sine waves to give the final speech output. The resulting synthetic waveform preserves the general waveform shape and is essentially perceptually indistinguishable from the original speech. Furthermore, in the presence of noise the perceptual characteristics of the speech as well as the noise are maintained. In addition, it was found that the representation was sufficiently general that high-quality reproduction was obtained for a larger class of inputs including: two overlapping, superposed speech waveforms; music waveforms; speech in musical backgrounds; and certain marine biologic sounds. Finally, the analysis/synthesis system forms the basis for new approaches to the problems of speech transformations including time-scale and pitch-scale modification, and midrate speech coding [8], [9].

Speech analysis/Synthesis based on a sinusoidal representation

We model the underlying probability density function of vectors in a database as a Gaussian mixture (GM) model. The model is employed for high rate vector quantization analysis and for design of vector quantizers. It is shown that the high rate formulas accurately predict the performance of model-based quantizers. We propose a novel method for optimizing GM model parameters for high rate performance, and an extension to the EM algorithm for densities having bounded support is also presented. The methods are applied to quantization of LPC parameters in speech coding and we present new high rate analysis results for band-limited spectral distortion and outlier statistics. In practical terms, we find that an optimal single-stage VQ can operate at approximately 3 bits less than a state-of-the-art LSF-based 2-split VQ.

Vector quantization based on Gaussian mixture models

We present an estimator-based, or soft, vector quantizer decoder for communication over a noisy channel. The decoder is optimal according to the mean-square error criterion, and Hadamard-based in the sense that a Hadamard transform representation of the vector quantizer is utilized in the implementation of the decoder. An efficient algorithm for optimal decoding is derived. We furthermore investigate suboptimal versions of the decoder, providing good performance at lower complexity. The issue of joint encoder-decoder design is considered both for optimal and suboptimal decoding. Results regarding the channel distortion and the structure of a channel robust code are also provided. Through numerical simulations, soft decoding is demonstrated to outperform hard decoding in several aspects.

Hadamard-based soft decoding for vector quantization over noisy channels

A procedure is suggested for improving LPC speech quality. The central theme is to introduce a parametric model of voiced excitation - a glottal source model. In the analysis this allows for a different method than the AR-estimation used in conventional LPC. Here, a method known as AR-X-estimation is used. A complete analysis and coding method is presented. It is found that the additional glottal parameters can be coded effectively such that the total bit rate is in the same range as for conventional LPC. The glottal LPC-vocoder does significantly improve synthesis quality as compared to standard LPC. It should be emphasized, however, that the glottal vocoder requires high quality speech as input, recorded in a phase linear system. Moreover, the computational complexity is high.

A glottal LPC-vocoder

In this paper, Gaussian mixture modeling is applied to error concealment for block-based packet video. A Gaussian mixture model for video data is obtained offline and is thereafter utilized online in order to restore lost blocks from spatial and temporal surrounding information. We propose estimators on closed form for missing data in the case of varying available neighboring contexts. Our error concealment strategy increases peak signal-to-noise ratio compared to previously proposed schemes. Examples of improved subjective visual quality by means of the proposed method are also supplied.

/pdf/packet-video-error-concealment-with-gaussian-mixture-models-4qjr8xh8id.pdf

Packet Video Error Concealment With Gaussian Mixture Models

A theoretical analysis of recursive speech spectrum coding, where predictive and finite state schemes are special cases, is presented. We evaluate the spectral distortion (SD) theoretically and design coders that minimize the SD. The analysis rests on three cornerstones: high-rate theory, PDF modeling, and an approximation of SD. A derivation of the mean L/sub 2/-norm distortion of a recursive quantizer operating at high rate is provided. Also, the distortion distribution is supplied. The evaluation of the distortion expressions requires a model of the joint PDF of two consecutive spectrum vectors. The LPC spectrum source considered here has outcomes in a bounded region, and this is taken into account in the choice of model and modeling algorithm. It is further shown how to approximate the SD with an L/sub 2/-norm measure. Combining the results, we show theoretically that 16 bits are needed to achieve an average SD of 1 dB when quantizing ten-dimensional (10-D) spectrum vectors using a first-order recursive scheme. A gain of six bits per frame is noted compared to memoryless quantization. These results rely on high-rate assumptions which are validated in experiments. There, actual high-rate optimal coders are designed and evaluated.

Recursive coding of spectrum parameters

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