torch-signal

• Fourier Transforms (real & complex) (1D, 2D, 3D)
• Cosine Transforms (1D, 2D, 3D)
• Short-time Fourier Transforms
• Spectrogram
• Hilbert Transform
• Complex Cepstral Analysis, Real Cepstrums

Quickstart

OSX (Homebrew):

brew install fftw

Ubuntu:

sudo apt-get install libfftw3

Install torch-signal:

luarocks install https://raw.github.com/soumith/torch-signal/master/rocks/signal-scm-1.rockspec

For documentation, go to: http://soumith.github.io/torch-signal/signal/

For examples, see tests/

keep the loaded C object around, so that it doesn't get garbage collected

complex.lua

All functions in here expect either a 2D Nx2 Complex tensor

signal.complex.poly(x)

Polynomial with specified roots

Function is super unoptimized

Undocumented methods

• signal.complex.angle(h)
• signal.complex.exp(h)
• signal.complex.abs(h)
• signal.complex.real(h)
• signal.complex.imag(h)
• signal.complex.conj(h)
• signal.complex.prod(h)
• signal.complex.cmul(a1,b1, noargcheck)
• signal.complex.dot(a,b)
• signal.complex.mm(a,b)
• signal.complex.diag(x)

signal.conv1d(input, kernel, stride)

1D valid convolution with stride

extramath.lua

some extra math functions

Undocumented methods

• signal.xmath.round(num)
• signal.xmath.log2(x)
• signal.xmath.nextpow2(x)

signal.fft(input)

1D FFT Takes Real inputs (1D tensor of N points) or complex inputs 2D tensor of (Nx2) size for N points

Output matches with matlab output

signal.ifft(input)

inverse 1D FFT Takes Real inputs (1D tensor of N points) or complex inputs 2D tensor of (Nx2) size for N points

Output matches with matlab output

signal.rfft(input)

real to complex dft. This function retains only the positive frequencies. Input is a 1D real tensor Output is 2D complex tensor of size (input:size(1)/2 + 1, 2)

signal.irfft(input)

complex to real dft. This function is the exact inverse of signal.rfft

signal.fft2(input)

2D FFT Takes Real inputs (2D tensor of NxM points) or complex inputs 3D tensor of (NxMx2) size for NxM points

Output matches with matlab output

signal.ifft2(input)

2D Inverse FFT Takes Real inputs (2D tensor of NxM points) or complex inputs 3D tensor of (NxMx2) size for NxM points

Output matches with matlab output

signal.fft3(input)

3D FFT Takes Real inputs (3D tensor of NxMxP points) or complex inputs 4D tensor of (NxMxPx2) size for NxMxP points

Output matches with matlab output

signal.ifft3(input)

3D Inverse FFT Takes Real inputs (3D tensor of NxMxP points) or complex inputs 4D tensor of (NxMxPx2) size for NxMxP points

Output matches with matlab output

signal.hann(L, flag)

returns an L-point Hann window in a 1D tensor. L must be a positive integer. When 'periodic' is specified, hann computes a length L+1 window and returns the first L points. flag: 'periodic' or 'symmetric'. 'symmetric' is default

Output matches with matlab output

signal.blackman(N, flag)

returns an N-point Blackman window in a 1D tensor. N must be a positive integer. When 'periodic' is specified, computes a length N+1 window and returns the first N points. flag: 'periodic' or 'symmetric'. 'symmetric' is default

Output matches with matlab output

signal.blackmanharris(N, flag)

returns an N-point minimum 4-term Blackman-Harris window in a 1D tensor. The window is minimum in the sense that its maximum sidelobes are minimized. N must be a positive integer.
flag: 'periodic' or 'symmetric'. 'symmetric' is default

Output matches with matlab output

signal.stft(input, window_size, window_stride, window_type)

1D complex short-time fourier transforms Run a window across your signal and calculate fourier transforms on that window. To make sure that the windows are not discontinuous at the edges, you can optionally apply a window preprocessor. The available window preprocessors are: hamming, hann, bartlett

signal.rstft(input, window_size, window_stride, window_type)

1D real short-time fourier transforms Run a window across your signal and calculate fourier transforms on that window. To make sure that the windows are not discontinuous at the edges, you can optionally apply a window preprocessor. rfft is used for fourier transform, so only the positive frequencies are retained The available window preprocessors are: hamming, hann, bartlett

signal.spectrogram(inp, window_size, window_stride)

Takes the rstft(x) and generates a pretty spectrogram by taking the magnitude of the stft, and applying a (natural log * 10) Also transposes the output, to have time on the X axis.

signal.unwrap(a, tol)

Correct phase angles to produce smoother phase plots
Unwrap radian phases by adding multiples of 2*pi as appropriate to remove jumps greater than tol. tol defaults to pi.

Output matches with matlab output

signal.rcunwrap(x)

unwraps the phase and removes phase corresponding to integer lag.

Output matches with matlab output

signal.rcwrap(y, nd)

Adds phase corresponding to integer lag

Output matches with matlab output

signal.cceps(x)

1D Complex cepstral analysis Returns the cepstrum and a phase shift factor "nd" that is useful to invert the signal back.

Output matches with matlab output

signal.icceps(xhat,nd)

1D Inverse Complex cepstral analysis. Takes in the outputs of cceps to produce the input signal back

Output matches with matlab output

signal.rceps(x)

Real cepstrum and minimum phase reconstruction The real cepstrum is the inverse Fourier transform of the real logarithm of the magnitude of the Fourier transform of a sequence.

Output matches with matlab output

signal.dct(input)

1D Discrete Cosine Transform (DCT) Takes Real inputs (1D tensor of N points)

To see what is exactly computed, see section REDFT10 over here: http://www.fftw.org/doc/1d-Real_002deven-DFTs-_0028DCTs_0029.html

signal.idct(input)

inverse 1D Discrete Cosine Transform (DCT) Takes Real inputs (1D tensor of N points)

To see what is exactly computed, see section REDFT01 over here: http://www.fftw.org/doc/1d-Real_002deven-DFTs-_0028DCTs_0029.html

signal.dct2(input)

2D Discrete Cosine Transform (DCT) Takes Real inputs (2D tensor of NxM points)

To see what is exactly computed, see section REDFT10 over here: http://www.fftw.org/doc/1d-Real_002deven-DFTs-_0028DCTs_0029.html

signal.idct2(input)

inverse 2D Discrete Cosine Transform (DCT) Takes Real inputs (2D tensor of NxM points)

To see what is exactly computed, see section REDFT01 over here: http://www.fftw.org/doc/1d-Real_002deven-DFTs-_0028DCTs_0029.html

signal.dct3(input)

3D Discrete Cosine Transform (DCT) Takes Real inputs (3D tensor of NxMXP points)

To see what is exactly computed, see section REDFT10 over here: http://www.fftw.org/doc/1d-Real_002deven-DFTs-_0028DCTs_0029.html

signal.idct3(input)

inverse 3D Discrete Cosine Transform (DCT) Takes Real inputs (3D tensor of NxMxP points)

To see what is exactly computed, see section REDFT01 over here: http://www.fftw.org/doc/1d-Real_002deven-DFTs-_0028DCTs_0029.html

signal.hilbert(xr)

Discrete-time analytic signal using Hilbert transform Takes 1D inputs

Output matches with matlab output

Undocumented methods

• signal.typecheck(input)

signal.wavelet.haar1d()

Haar wavelet (1D) return the phi and psi functions of a haar wavelet

signal.wavelet.daubechies1d()

Daubechies wavelet (1D) return the phi and psi functions of a daubechies wavelet

signal.wavelet.dwt1d(input, phi, psi, maxlevels)

Calculates the discrete wavelet transform, given the phi and psi functions phi and psi are functions that take the input signal and give out the scaled signal, and the wavelet coefficients respectively.

input - input signal \phi φ(x) - scaling function \psi ψ(x) - wavelet function [maxlevels] - maximum number of levels to recurse