Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
Convex Optimization
Error Correction Coding: Mathematical Methods and Algorithms
Error Correction Coding: Mathematical Methods and Algorithms
Nonlinear Time Series Analysis
Nonlinear Time Series Analysis
Discrete-time speech signal processing: principles and practice
Discrete-time speech signal processing: principles and practice
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Convolution theorems for linear transforms
IEEE Transactions on Signal Processing
Time-Varying Autoregressions in Speech: Detection Theory and Applications
IEEE Transactions on Audio, Speech, and Language Processing
Data compression and harmonic analysis
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Nonlinear speech coding model based on genetic programming
Applied Soft Computing
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Classical digital speech signal processing assumes linearity, time-invariance, and Gaussian random variables (LTI-Gaussian theory). In this article, we address the suitability of these mathematical assumptions for realistic speech signals with respect to the biophysics of voice production, finding that the LTI-Gaussian approach has some important accuracy and computational efficiency shortcomings in both theory and practice. Next, we explore the consequences of relaxing the assumptions of time-invariance and Gaussianity, which admits certain potentially useful techniques, including wavelet and sparse representations in computational harmonic analysis, but rules out Fourier analysis and convolution, which could be a disadvantage. Then, we focus on methods that retain time-invariance alone, which admits techniques from nonlinear time series analysis and Markov chains, both of which have shown promise in biomedical applications. We highlight recent examples of non-LTI-Gaussian digital speech signal processing in the literature, and draw conclusions for future prospects in this area.