Think DSP: Digital Signal Processing in Python

by Allen Downey

Overview

If you understand basic mathematics and know how to program with Python, you're ready to dive into signal processing. While most resources start with theory to teach this complex subject, this practical book introduces techniques by showing you how they're applied in the real world. In the first chapter alone, you'll be able to decompose a sound into its harmonics, modify the harmonics, and generate new sounds.

Author Allen Downey explains techniques such as spectral decomposition, filtering, convolution, and the Fast Fourier Transform. This book also provides exercises and code examples to help you understand the material.

You'll explore:

• Periodic signals and their spectrums
• Harmonic structure of simple waveforms
• Chirps and other sounds whose spectrum changes over time
• Noise signals and natural sources of noise
• The autocorrelation function for estimating pitch
• The discrete cosine transform (DCT) for compression
• The Fast Fourier Transform for spectral analysis
• Relating operations in time to filters in the frequency domain
• Linear time-invariant (LTI) system theory
• Amplitude modulation (AM) used in radio

Other books in this series include Think Stats and Think Bayes, also by Allen Downey.

Product Details

ISBN-13:	9781491938454
Publisher:	O'Reilly Media, Incorporated
Publication date:	08/06/2016
Pages:	165
Product dimensions:	6.90(w) x 9.00(h) x 0.50(d)

About the Author

Allen Downey is a Professor of Computer Science at Olin College of Engineering. He has taught at Wellesley College, Colby College and U.C. Berkeley. He has a Ph.D. in Computer Science from U.C. Berkeley and Master's and Bachelor's degrees from MIT.

Table of Contents

Preface vii

1 Sounds and Signals 1

Periodic Signals 1

Spectral Decomposition 3

Signals 5

Reading and Writing Waves 7

Spectrums 7

Wave Objects 8

Signal Objects 9

Exercises 11

2 Harmonics 13

Triangle Waves 13

Square Waves 16

Aliasing 17

Computing the Spectrum 20

Exercises 21

3 Non-Periodic Signals 25

Linear Chirp 25

Exponential Chirp 28

Spectrum of a Chirp 29

Spectrogram 30

The Gabor Limit 31

Leakage 32

Windowing 33

Implementing Spectrograms 35

Exercises 36

4 Noise 39

Uncorrelated Noise 39

Integrated Spectrum 42

Brownian Noise 43

Pink Noise 46

Gaussian Noise 48

Exercises 50

5 Autocorrelation 53

Correlation 53

Serial Correlation 56

Autocorrelation 57

Autocorrelation of Periodic Signals 58

Correlation as Dot Product 61

Using NumPy 62

Exercises 64

6 Discrete Cosine Transform 65

Synthesis 66

Synthesis with Arrays 66

Analysis 68

Orthogonal Matrices 69

DCT-IV 71

Inverse DCT 72

The Dct Class 73

Exercises 74

7 Discrete Fourier Transform 77

Complex Exponentials 77

Complex Signals 79

The Synthesis Problem 80

Synthesis with Matrices 82

The Analysis Problem 84

Efficient Analysis 85

DFT 86

The DFT Is Periodic 87

DFT of Real Signals 88

Exercises 90

8 Filtering and Convolution 91

Smoothing 91

Convolution 94

The Frequency Domain 95

The Convolution Theorem 97

Gaussian Filter 98

Efficient Convolution 100

Efficient Autocorrelation 101

Exercises 103

9 Differentiation and Integration 105

Finite Differences 105

The Frequency Domain 107

Differentiation 108

Integration 111

Cumulative Sum 112

Integrating Noise 115

Exercises 116

10 Lit Systems 119

Signals and Systems 119

Windows and Filters 121

Acoustic Response 122

Systems and Convolution 125

Proof of the Convolution Theorem 128

Exercises 130

11 Modulation and Sampling 133

Convolution with Impulses 133

Amplitude Modulation 134

Sampling 137

Aliasing 140

Interpolation 143

Summary 146

Exercises 147

Index 149