Index
A
- abs, Complex Exponentials
- acoustic response, Acoustic Response
- aliasing, Harmonics, Aliasing, Exercises, DFT of Real Signals, Modulation and Sampling, Exercises
- AM, Amplitude Modulation
- amplifier, Signals and Systems
- amplitude, Spectral Decomposition, Signal Objects, Computing the Spectrum, Complex Exponentials
- amplitude modulation, Amplitude Modulation
- Anaconda, Using the Code
- analog-to-digital converter, Sampling
- analysis, Discrete Cosine Transform, Synthesis, The Analysis Problem
- angle, Computing the Spectrum, Complex Exponentials, Complex Exponentials
- anti-aliasing filter, Exercises
- aplay, Reading and Writing Waves
- Audio widget, Spectrums
- autocorrelation, Autocorrelation, Autocorrelation, Efficient Autocorrelation
- autocorrelation function, Autocorrelation of Periodic Signals
B
- band stop filter, Spectrums
- Bartlett’s method, Exercises
- bias, Pink Noise, Integration
- Binder, Using the Code
- bit depth, Sampling
- BitCoin, Exercises, Exercises
- Boccherini, Periodic Signals
- boxcar window, Gaussian Filter
- brick wall filter, Interpolation
- Brownian noise, Uncorrelated Noise, Brownian Noise, Serial Correlation, Finite Differences, Integrating Noise
C
- carrier wave, Amplitude Modulation
- Cartesian coordinate, Computing the Spectrum
- characterizing a system, Signals and Systems
- chirp, Linear Chirp, Exercises
- circuits, Signals and Systems
- circular convolution, Convolution, Exercises
- cloning the repo, Using the Code
- complex amplitude, Synthesis with Matrices
- complex conjugate, Efficient Analysis
- complex exponential, Complex Exponentials, Complex Signals, Proof of the Convolution Theorem
- complex number, Computing the Spectrum, Complex Exponentials
- complex plane, Complex Exponentials
- complex signal, The Synthesis Problem
- complex sinusoid, Complex Signals, Differentiation
- component, Signals, Proof of the Convolution Theorem
- compression, Exercises
- contributors, Contributor List
- convolution, Filtering and Convolution, Convolution, Systems and Convolution, Convolution with Impulses, Amplitude Modulation
- Convolution Theorem, Filtering and Convolution, The Convolution Theorem, Cumulative Sum, Systems and Convolution, Proof of the Convolution Theorem
- correlation, Brownian Noise, Pink Noise, Correlation, Correlation as Dot Product, The DFT Is Periodic
- correlation matrix, Correlation
- cosine, Signals
- CosSignal, Signals
- cross-correlation, Convolution, Efficient Autocorrelation
- cubic waveform, Exercises
- cumsum, Linear Chirp, Exercises
- cumulative sum, Linear Chirp, Cumulative Sum, Integrating Noise
- cycle, Periodic Signals, Triangle Waves
D
- Danielson–Lanczos lemma, Exercises
- DCT, Discrete Cosine Transform
- Dct, The Dct Class
- DCT-IV, DCT-IV
- demodulation, Amplitude Modulation
- derivative, Linear Chirp, Differentiation
- DFT, Spectral Decomposition, Triangle Waves, Discrete Cosine Transform, Discrete Fourier Transform, DFT, Exercises, Proof of the Convolution Theorem
- diff, Exercises
- differential equations, Signals and Systems
- differentiate, Exercises
- differentiation, Differentiation and Integration, Differentiation
- discontinuity, Leakage
- Discrete Cosine Transform, Discrete Cosine Transform
- Discrete Fourier Transform (see DFT)
- dominant frequency, Spectral Decomposition
- dot product, Correlation as Dot Product, Synthesis with Arrays
E
- eigenfunction, Differentiation, Proof of the Convolution Theorem
- eigenvalue, Differentiation, Proof of the Convolution Theorem
- equal temperament, Spectral Decomposition
- Euler, Complex Exponentials
- Euler’s formula, Complex Exponentials
- exponential chirp, Exponential Chirp
- Eye of Sauron, Spectrum of a Chirp
F
- Facebook stock price, Smoothing, Efficient Convolution
- Fast Fourier Transform (see FFT)
- FFT, Spectral Decomposition, Computing the Spectrum, Exercises, Efficient Convolution
- fft, Computing the Spectrum
- filter, Pink Noise, The Convolution Theorem, The Frequency Domain, Differentiation, Integration, Windows and Filters
- finite difference, The Frequency Domain
- floating-point, DCT-IV
- folding frequency, Aliasing, DFT of Real Signals
- fork, Using the Code
- frame, Signals
- Freesound, Contributor List, Exercises, Exercises, Autocorrelation of Periodic Signals
- frequency, Periodic Signals, Signal Objects, Linear Chirp
- frequency component, Signals, Synthesis, Analysis
- frequency domain, The Convolution Theorem, The Frequency Domain, Amplitude Modulation
- frequency resolution, The Gabor Limit, Autocorrelation of Periodic Signals
- full DFT, DFT of Real Signals
- fundamental frequency, Spectral Decomposition, Triangle Waves
G
- Gabor limit, The Gabor Limit, Autocorrelation of Periodic Signals
- gamma function, Complex Exponentials
- Gaussian filter, Gaussian Filter
- Gaussian noise, Uncorrelated Noise, Gaussian Noise
- Gaussian signal, Exercises
- Gaussian window, Exercises, Exercises
- Geiger counter, Exercises
- Git, Using the Code
- GitHub, Using the Code
- glissando, Exercises
- gunshot, Acoustic Response
H
- Hamming window, Windowing, Exercises
- harmonic structure, Harmonics, Triangle Waves, Square Waves, Exercises
- harmonics, Spectral Decomposition, Triangle Waves, DFT of Real Signals
- Hart, Vi, Exercises
- Hertz, Periodic Signals
- high-pass filter, Spectrums, Finite Differences
I
- identity matrix, Orthogonal Matrices, Efficient Analysis
- imaginary number, Complex Exponentials
- impulse, Signals and Systems, Systems and Convolution, Systems and Convolution, Convolution with Impulses, Amplitude Modulation
- impulse response, Signals and Systems, Exercises
- impulse train, Sampling
- input, Signals and Systems
- installation, Using the Code
- integral, Linear Chirp
- integrate, Exercises
- integrated spectrum, Integrated Spectrum
- integration, Differentiation and Integration, Integration, Cumulative Sum
- interpolation, Interpolation
- interval, Exponential Chirp
- inverse DCT, Inverse DCT
- inverse DFT, DFT
J
- Jupyter, Using the Code, Spectrums
L
- lag, Serial Correlation, Autocorrelation
- leakage, Leakage, Smoothing
- linear algebra, Synthesis with Arrays
- linear system, Signals and Systems
- log-log scale, Brownian Noise, Integrating Noise
- logspace, Exponential Chirp
- long-range dependence, Autocorrelation
- low-pass filter, Spectrums, Pink Noise, The Frequency Domain, Gaussian Filter, Windows and Filters, Amplitude Modulation
- LTI system, Signals and Systems
M
- magnitude, Computing the Spectrum, Complex Exponentials
- major third, Spectral Decomposition
- matplotlib, Using the Code
- matrix, Synthesis with Arrays
- matrix inverse, Orthogonal Matrices
- matrix multiplication, Synthesis with Matrices
- mechanical systems, Signals and Systems
- missing fundamental, Exercises
- modf, Triangle Waves
- modulation, Amplitude Modulation
- Montgomery, Chris, Exercises
- moving average, Smoothing
N
- NaN, Integration
- nbviewer, Using the Code
- noise, Noise, Exercises
- non-periodic signal, Non-Periodic Signals, Exercises
- normal probability plot, Gaussian Noise
- normalize, The Dct Class, Efficient Autocorrelation
- NumPy, Using the Code, Using NumPy, Convolution
- Nyquist, Interpolation
- Nyquist frequency, Aliasing
O
- octave, Spectral Decomposition, Exponential Chirp
- operator, Differentiation
- orthogonal matrix, Orthogonal Matrices, DCT-IV, Efficient Analysis
- outer product, Synthesis with Arrays, Synthesis with Matrices
- output, Signals and Systems
P
- padding, Smoothing, Efficient Autocorrelation, Exercises
- Pandas, Efficient Convolution, Finite Differences
- parabola, Cumulative Sum
- Pearson’s correlation, Correlation
- perfect fifth, Spectral Decomposition
- period, Periodic Signals, Square Waves
- periodic, Leakage
- periodic DFT, The DFT Is Periodic
- periodic signal, Periodic Signals, Autocorrelation of Periodic Signals
- phase, Linear Chirp
- phase offset, Signals, Signal Objects, Computing the Spectrum, Correlation, Exercises, Complex Signals
- pink noise, Uncorrelated Noise, Pink Noise, Exercises, Serial Correlation, Efficient Autocorrelation
- pitch, Periodic Signals
- pitch estimation, Autocorrelation of Periodic Signals
- pitch perception, Exercises
- pitch tracking, Exercises
- Poisson noise, Exercises
- polar coordinate, Computing the Spectrum
- power, Uncorrelated Noise, Brownian Noise, Exercises
- power series, Complex Exponentials
- power spectrum, Brownian Noise
- proof, Proof of the Convolution Theorem
- Python 2, Using the Code
- Python 3, Using the Code
R
- random, Uncorrelated Noise, Pink Noise
- random walk, Brownian Noise
- real DFT, DFT of Real Signals
- real FFT, Computing the Spectrum
- red noise, Brownian Noise
- repository, Using the Code
- resolution, The Gabor Limit
- response, Systems and Convolution
S
- sample, Signals, Aliasing, Systems and Convolution
- sampling, Modulation and Sampling, Sampling
- Sampling Theorem, Modulation and Sampling, Interpolation
- sawtooth chirp, Exercises
- sawtooth waveform, Exercises, Exercises, Systems and Convolution
- scale, Wave Objects, Systems and Convolution, Exercises, Convolution with Impulses
- scientific pitch notation, Periodic Signals
- SciPy, Using the Code, Exercises
- segment, Signals
- serial correlation, Serial Correlation
- Shannon, Interpolation
- shift, Wave Objects, Serial Correlation, Smoothing, Systems and Convolution, Exercises, Convolution with Impulses
- Short-Time Fourier Transform, Spectrogram
- sidelobe, Gaussian Filter
- signal, Sounds and Signals
- Signal, Signals, Signal Objects
- signal processing, Preface
- sinc function, Interpolation
- sine, Signals
- SinSignal, Signals
- sinusoid, Periodic Signals
- Sinusoid, Signals, Signal Objects
- smoothing, Smoothing, The Convolution Theorem
- Soft Murmur, Exercises
- sound, Sounds and Signals
- sparse array, Exercises
- spectral analysis, Discrete Cosine Transform
- spectral decomposition, Spectral Decomposition, Differentiation, Signals and Systems
- spectral leakage, Leakage, Smoothing
- spectral method, Differentiation
- spectrogram, Non-Periodic Signals, Spectrogram, Implementing Spectrograms, Exercises
- spectrum, Signals, Triangle Waves, Spectrum of a Chirp, Uncorrelated Noise, The Frequency Domain, Sampling
- Spectrum, Spectrums
- square matrix, Analysis
- square waveform, Square Waves, Exercises, Smoothing
- standard deviation, Correlation
- standardizing, Using NumPy
- static, Uncorrelated Noise
- STFT, Spectrogram
- stock prices, Integrating Noise
- stretch function, Exercises
- SumSignal, Signals
- symmetric matrix, Orthogonal Matrices
- synthesis, Exercises, Discrete Cosine Transform, Synthesis, The Synthesis Problem
- system, Signals and Systems
T
- temperament, Spectral Decomposition
- timbre, Periodic Signals
- time domain, The Convolution Theorem, Finite Differences
- time resolution, The Gabor Limit
- time-invariant system, Signals and Systems
- timestep, Signals
- transducer, Sounds and Signals
- transfer function, Acoustic Response, Systems and Convolution, Systems and Convolution
- transpose, Orthogonal Matrices, Efficient Analysis
- triangle waveform, Triangle Waves, Exercises, The Dct Class
- trombone, Exercises
- tuning fork, Periodic Signals
U
- UG noise, Gaussian Noise
- unbias, Triangle Waves
- uncorrelated noise, Uncorrelated Noise
- uniform noise, Uncorrelated Noise
- unitary matrix, Efficient Analysis
- UU noise, Uncorrelated Noise, Serial Correlation
V
- vector, Orthogonal Matrices
- video, Exercises
- violin, Spectral Decomposition, Acoustic Response
- virtual machine, Using the Code
- Voss–McCartney algorithm, Exercises
- vowel, Exercises
W
- WAV file, Reading and Writing Waves, Sampling
- Wave, Signals, Wave Objects
- waveform, Periodic Signals
- white noise, Integrated Spectrum, Finite Differences, Signals and Systems
- window, Leakage, Windowing, Smoothing, Exercises, The Frequency Domain, Windows and Filters
- windowing, Windowing
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