Fundamentals Of Statistical Signal Processing

This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given

Linear prediction: A tutorial review

From the Publisher:
This book takes an empirical approach to language processing, based on applying statistical and other machine-learning algorithms to large corpora.Methodology boxes are included in each chapter. Each chapter is built around one or more worked examples to demonstrate the main idea of the chapter. Covers the fundamental algorithms of various fields, whether originally proposed for spoken or written language to demonstrate how the same algorithm can be used for speech recognition and word-sense disambiguation. Emphasis on web and other practical applications. Emphasis on scientific evaluation. Useful as a reference for professionals in any of the areas of speech and language processing.

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Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition

We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplicity, extremely fast calculation, robustness, and invariance with respect to nonlinear monotonous transformations.

Permutation entropy: a natural complexity measure for time series.

Data hiding, a form of steganography, embeds data into digital media for the purpose of identification, annotation, and copyright. Several constraints affect this process: the quantity of data to be hidden, the need for invariance of these data under conditions where a "host" signal is subject to distortions, e.g., lossy compression, and the degree to which the data must be immune to interception, modification, or removal by a third party. We explore both traditional and novel techniques for addressing the data-hiding process and evaluate these techniques in light of three applications: copyright protection, tamper-proofing, and augmentation data embedding.

Techniques for data hiding

We discuss a computational algorithm for numerically evaluating the z-transform of a sequence of N samples. This algorithm has been named the chirp z-transform algorithm. Using this algorithm one can efficiently evaluate the z-transform at M points in the z-plane which lie on circular or spiral contours beginning at any arbitrary point in the z-plane. The angular spacing of the points is an arbitrary constant; M and N are arbitrary integers. The algorithm is based on the fact that the values of the z-transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N + M) log 2 (N + M) as opposed to being proportional to N · M for direct evaluation of the z-transform at M points. Applications discussed include: enhancement of poles in spectral analysis, high resolution narrow-band frequency analysis, interpolation of band-limited waveforms, and the conversion of a base 2 fast Fourier transform program into an arbitrary radix fast Fourier transform program.

The chirp z-transform algorithm and its application

A system for automatically estimating the lowest three formants and the pitch period of voiced speech is presented. The system is based on a digital computation of the cepstrum (defined as the inverse transform of the log magnitude of the z‐transform). The pitch period estimate and smoothed log magnitude are obtained from the cepstrum. Formants are estimated from the smoothed spectral envelope using constraints on formant frequency ranges and relative levels of spectral peaks at the formant frequencies. These constraints allow the detection of cases where two formants are too close together in frequency to be resolved in the initial spectral envelope. In these cases, a new spectral analysis algorithm (the chirp z‐transform algorithm) allows the efficient computation of a narrow‐band spectrum in which the formant resolution is enhanced. Formant and pitch period data obtained by the analysis system are used to control a digital formant synthesizer. Results, in the form of spectrograms, are presented to illu...

System for automatic formant analysis of voiced speech.

Theory and Applications of Digital Speech Processing is ideal for graduate students in digital signal processing, and undergraduate students in Electrical and Computer Engineering. With its clear, up-to-date, hands-on coverage of digital speech processing, this text is also suitable for practicing engineers in speech processing. This new text presents the basic concepts and theories of speech processing with clarity and currency, while providing hands-on computer-based laboratory experiences for students. The material is organized in a manner that builds a strong foundation of basics first, and then concentrates on a range of signal processing methods for representing and processing the speech signal.

Theory and Applications of Digital Speech Processing

1. Introduction. Mathematical Representation of Signals. Mathematical Representation of Systems. Thinking about Systems. 2. Sinusoids. Tuning Fork Experiment. Review of Sine and Cosine Functions. Sinusoidal Signals. Sampling and Plotting Sinusoids. Complex Exponentials and Phasors. Phasor Addition. Physics of the Tuning Fork. Time Signals: More Than Formulas. 3. Spectrum Representation. The Spectrum of a Sum of Sinusoids. Beat Notes. Periodic Waveforms. More Periodic Signals. Fourier Series Analysis and Synthesis. Time-Frequency Spectrum. Frequency Modulation: Chirp Signals. 4. Sampling and Aliasing. Sampling. Spectrum View of Sampling and Reconstruction. Strobe Demonstration. Discrete-to-Continuous Conversion. The Sampling Theorem. 5. FIR Filters. Discrete-Time Systems. The Running Average Filter. The General FIR Filter. Implementation of FIR Filters. Linear Time-Invariant (LTI) Systems. Convolution and LTI Systems. Cascaded LTI Systems. Example of FIR Filtering. 6. Frequency Response of FIR Filters. Sinusoidal Response of FIR Systems. Superposition and the Frequency Response. Steady State and Transient Response. Properties of the Frequency Response. Graphical Representation of the Frequency Response. Cascaded LTI Systems. Running-Average Filtering. Filtering Sampled Continuous-Time Signals. 7. z-Transforms. Definition of the z-Transform. The z-Transform and Linear Systems. Properties of the z-Transform. The z-Transform as an Operator. Convolution and the z-Transform. Relationship between the z -Domain and the w-Domain. Useful Filters. Practical Bandpass Filter Design. Properties of Linear Phase Filters. 8. IIR Filters. The General IIR Difference Equation. Time-Domain Response. System Function of an IIR Filter. Poles and Zeros. Frequency Response of an IIR Filter. Three Domains. The Inverse z-Transform and Some Applications. Steady-State Response and Stability. Second-Order Filters. Frequency Response of Second-Order IIR Filter. Example of an IIR Lowpass Filter. 9. Continuous-Time Signals and LTI Systems. Continuous-Time Signals. The Unit Impulse. Continuous-Time Systems. Linear Time-Invariant Systems. Impulse Responses of Basic LTI Systems. Convolution of Impulses. Evaluating Convolution Integrals. Properties of LTI Systems. Using Convolution to Remove Multipath Distortion. 10. The Frequency Response. The Frequency Response Function for LTI Systems. Response to Real Sinusoidal Signals. Ideal Filters. Application of Ideal Filters. Time-Domain or Frequency-Domain? 11. Continuous-Time Fourier Transform. Definition of the Fourier Transform. The Fourier Transform and the Spectrum. Existence and Convergence of the Fourier Transform. Examples of Fourier Transform Pairs. Properties of Fourier Transform Pairs. The Convolution Property. Basic LTI Systems. The Multiplication Property. Table of Fourier Transform Properties and Pairs. Using the Fourier Transform for Multipath Analysis. 12. Filtering, Modulation, and Sampling. Linear Time-Invariant Systems. Sinewave Amplitude Modulation. Sampling and Reconstruction. 13. Computing the Spectrum. Finite Fourier Sum. Too Many Fourier Transforms? Time-windowing. Analysis of a Sum of Sinusoids. Discrete Fourier Transform. Spectrum Analysis of Finite-Length Signals. Spectrum Analysis of Periodic Signals. The Spectrogram. The Fast Fourier Transform (FFT). Appendix A: Complex Numbers. Notation for Complex Numbers. Euler's Formula. Algebraic Rules for Complex Numbers. Geometric Views of complex Operations. Powers and Roots. Appendix B: Programming in MATLAB. MATLAB Help. Matrix Operations and Variables. Plots and Graphics. Programming Constructs. MATLAB Scripts. Writing a MATLAB Function. Programming Tips. Appendix C: Laboratory Projects. Introduction to MATLAB. Encoding and Decoding Touch-Tone Signals. Two Convolution GUIs. Appendix D: CD-ROM Demos. Index.

Signal Processing First

From the Publisher:

Presents many computer-based problems that can be done in conjunction with a course in DSP theory.

Projects relate to practical systems and implementations so the reader can learn and understand how DSP is applied.

Includes projects and exercises, which make full use of the power of MATLAB v5 to explore conceptual, analytical, and computational issues in digital signal processing.
Many projects provide hints to introduce pitfalls, limitations and tricks for getting the most out of MATLAB v5.
Discusses both the power and limitations of MATLAB v5 functions and regularly explores the issue of using built-in functions versus developing code to solve problems.
Exercises consistently reinforce important problem solving behaviors, such as verifying results, experimenting with parameters as a means of building understanding and intuition, exploring the realism of formulations, comparing theoretical and numerical or measured results, and developing predictions and then comparing them to actual results.

Ronald W. Schafer

Papers

The chirp z-transform algorithm and its application

System for automatic formant analysis of voiced speech.

Theory and Applications of Digital Speech Processing

Signal Processing First

Computer-Based Exercises for Signal Processing Using Matlab