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Table of Contents

Basics: The Moving Average Simple Low-Pass, High-Pass, and Gaussian Filters Signals and Systems Linear Time-Invariant (LTI) Systems Impulse Response and Convolution Fourier Transform and Inverse Fourier Transform Continuous vs. Discrete Periodic Signals: Sampling and Quantization Signals: Aliasing and the Nyquist Frequency Window Shapes and Sizes Magnitude, Phase, and the Complex Plane Magnitude Spectra and Spectrograms Harmonics and Resonances Resonance Frequencies, Bandwidths, and Magnitude Curves in the Complex Plane Laplace and z Transforms Resonance Filters and Klatt-Type Speech Synthesis Cepstral Analysis Images: Image Smoothing: Sobel, Median, and Gaussian Filters Edge Detection Morphological Filters Image Segmentation
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Introduction

 This blog is about how to do speech science - how to collect, visualize, analyze, and understand speech data. A lot of speech data are signals such as microphone recordings, but image data are increasingly common in speech science, and we therefore need tools to work with both signals and images. We will start with smoothing operations, beginning with moving averages. The moving average will provide us with a conceptually simple and - generally - familiar analysis tool, which we will then expand upon and generalize from. Along the way, we will see that the generalized moving average is an incredibly powerful tool - and one that relies on nothing more than arithmetic. (We will make use of more than arithmetic as we learn how to generalize the moving average, but the final results will always be expressible in simple arithmetic terms - terms that a computer can work with!) The "generalized moving average" is not a technical term in the field that I have ever heard, although I
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Preface

This blog is a place for me to work on an idea I have for a book on speech science, with an emphasis on presenting signal and image processing tools for analyzing speech, and explaining how they work. The goal is to produce a resource that will be helpful to a broad range of students and researchers pursuing the study of speech communication, including linguists, speech-language pathologists, cognitive scientists, and computer scientists. Along the way, I aim to synthesize at least a portion of the current state of knowledge about speech communication, with the hope that these materials could also be used as a textbook in undergraduate or graduate level speech science, motor speech, or phonetics classes. For now, I will assume the MATLAB scripting language when implementing the analysis tools that will be presented in this blog. If this project ends up turning into a book, I think I might like to provide code examples in Python and R as well as MATLAB... but we'll see. As for the q
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