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Book Description

Table of Contents

- Preface
- Who is this book for?
- Using the code

- Sounds and signals
- Periodic signals
- Spectral decomposition
- Signals
- Reading and writing Waves
- Spectrums
- Wave objects
- Signal objects
- Exercises

- Harmonics
- Triangle waves
- Square waves
- Aliasing
- Computing the spectrum
- Exercises

- Non-periodic signals
- Linear chirp
- Exponential chirp
- Spectrum of a chirp
- Spectrogram
- The Gabor limit
- Leakage
- Windowing
- Implementing spectrograms
- Exercises

- Noise
- Uncorrelated noise
- Integrated spectrum
- Brownian noise
- Pink Noise
- Gaussian noise
- Exercises

- Autocorrelation
- Correlation
- Serial correlation
- Autocorrelation
- Autocorrelation of periodic signals
- Correlation as dot product
- Using NumPy
- Exercises

- Discrete Cosine Transform
- Synthesis
- Synthesis with arrays
- Analysis
- Orthogonal matrices
- DCT-IV
- Inverse DCT
- The Dct class
- Exercises

- Discrete Fourier Transform
- Complex exponentials
- Complex signals
- The synthesis problem
- Synthesis with matrices
- The analysis problem
- Efficient analysis
- DFT
- The DFT is periodic
- DFT of real signals
- Exercises

- Filtering and Convolution
- Smoothing
- Convolution
- The frequency domain
- The Convolution Theorem
- Gaussian filter
- Efficient convolution
- Efficient autocorrelation
- Exercises

- Differentiation and Integration
- Finite differences
- The frequency domain
- Differentiation
- Integration
- Cumulative sum
- Integrating noise
- Exercises

- LTI systems
- Signals and systems
- Windows and filters
- Acoustic response
- Systems and convolution
- Proof of the Convolution Theorem
- Exercises

- Modulation and sampling
- Convolution with impulses
- Amplitude modulation
- Sampling
- Aliasing
- Interpolation
- Summary
- Exercises

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