This book introduces readers to the novel concept of variable span speech enhancement filters, and demonstrates how it can be used for effective noise reduction in various ways. Further, the book provides the accompanying Matlab code, allowing readers to easily implement the main ideas discussed. Variable span filters combine the ideas of optimal linear filters with those of subspace methods, as they involve the joint diagonalization of the correlation matrices of the desired signal and the noise. The book shows how some well-known filter designs, e.g. the minimum distortion, maximum signal-to-noise ratio, Wiener, and tradeoff filters (including their new generalizations) can be obtained using the variable span filter framework. It then illustrates how the variable span filters can be applied in various contexts, namely in single-channel STFT-based enhancement, in multichannel enhancement in both the time and STFT domains, and, lastly, in time-domain binaural enhancement. In these contexts, the properties of these filters are analyzed in terms of their noise reduction capabilities and desired signal distortion, and the analyses are validated and further explored in simulations.

This textbook presents an introduction to signal processing for audio applications. The author's approach posits that math is at the heart of audio processing and that it should not be simplified. He thus retains math as the core of signal processing and includes concepts of difference equations, convolution, and the Fourier Transform. Each of these is presented in a context where they make sense to the student and can readily be applied to build artifacts. Each chapter in the book builds on the previous ones, building a linear, coherent story. The book starts with a definition of sound and goes on to discuss digital audio signals, filters, The Fourier Transform, audio effects, spatial effects, audio equalizers, dynamic range control, and pitch estimation. The exercises in each chapter cover the application of the concepts to audio signals. The exercises are made specifically for Pure Data (Pd) although traditional software, such as MATLAB, can be used. The book is intended for students in media technology bachelor programs. The book is based on material the author developed teaching on the topic over a number of years.

This book introduces readers to the novel concept of variable span speech enhancement filters, and demonstrates how it can be used for effective noise reduction in various ways. Further, the book provides the accompanying Matlab code, allowing readers to easily implement the main ideas discussed. Variable span filters combine the ideas of optimal linear filters with those of subspace methods, as they involve the joint diagonalization of the correlation matrices of the desired signal and the noise. The book shows how some well-known filter designs, e.g. the minimum distortion, maximum signal-to-noise ratio, Wiener, and tradeoff filters (including their new generalizations) can be obtained using the variable span filter framework. It then illustrates how the variable span filters can be applied in various contexts, namely in single-channel STFT-based enhancement, in multichannel enhancement in both the time and STFT domains, and, lastly, in time-domain binaural enhancement. In these contexts, the properties of these filters are analyzed in terms of their noise reduction capabilities and desired signal distortion, and the analyses are validated and further explored in simulations.