Digital Signal Processing

The CR-Nimble library has some handy digital signal processing routines implemented in JAX. They are available as part of the cr.nimble.dsp package.

Signal Energy

energy(data[, axis])

Computes the energy of the signal along the specified axis

Thresholding

hard_threshold(x, K)	Returns the indices and corresponding values of largest K non-zero entries in a vector x
hard_threshold_sorted(x, K)	Returns the sorted indices and corresponding values of largest K non-zero entries in a vector x
hard_threshold_by(x, t)	Sets all entries in x to be zero which are less than t in magnitude
largest_indices_by(x, t)	Returns the locations of all entries in x which are larger than t in magnitude
energy_threshold(signal, fraction)	Keeps only as much coefficients in signal so as to capture a fraction of signal energy
hard_threshold_tau(x, tau)	Hard thresholding as per [CCSW14]
soft_threshold_tau(x, tau)	Soft thresholding as per [CCSW14]
half_threshold_tau(x, tau)	Half thresholding as per [CCSW14]
hard_threshold_percentile(x, perc)	Percentile hard thresholding as per [CCSW14]
soft_threshold_percentile(x, perc)	Percentile soft thresholding as per [CCSW14]
half_threshold_percentile(x, perc)	Percentile half thresholding as per [CCSW14]
gamma_to_tau_half_threshold(gamma)	Converts gamma to tau for half thresholding as per [CCSW14]
gamma_to_tau_hard_threshold(gamma)	Converts gamma to tau for hard thresholding as per [CCSW14]

Scaling

scale_to_0_1(x)	Scales a signal to the range of 0 and 1
scale_0_mean_1_var(data[, axis])	Normalizes a data vector (data - mu) / sigma

Quantization

quantize_1(x, n)

Quantizes a signal to n bits where signal values are bounded by 1

Spectrum Analysis

norm_freq(frequency, sampling_rate)	Returns the normalized frequency
frequency_spectrum(x[, dt])	Frequency spectrum of 1D data using FFT
power_spectrum(x[, dt])	Power spectrum of 1D data using FFT

Interpolation

interpft(x, N)

Interpolates x to n points in Fourier Transform domain

Windowing

sliding_windows_rw(x, wlen, overlap)	Converts a signal into sliding windows (per row) with the specified overlap
sliding_windows_cw(x, wlen, overlap)	Converts a signal into sliding windows (per column) with the specified overlap

Sparse Signals

Following functions analyze, transform, or construct signals which are known to be sparse.

nonzero_values(x)	Returns the values of non-zero entries in x
nonzero_indices(x)	Returns the indices of non-zero entries in x
support(x)	Returns the indices of non-zero entries in x
largest_indices(x, K)	Returns the indices of K largest entries in x by magnitude
sparse_approximation(x, K)	Keeps only largest K non-zero entries by magnitude in a vector x
build_signal_from_indices_and_values(length, …)	Builds a sparse signal from its non-zero entries (specified by their indices and values)

Matrices of Sparse Signals

Following functions analyze, transform, or construct collections of sparse signals organized as matrices.

randomize_rows(key, X)	Randomizes the rows in X
randomize_cols(key, X)	Randomizes the columns in X

Sparse representation matrices (row-wise)

take_along_rows(X, indices)	Picks K entries from each row of X specified by indices matrix
largest_indices_rw(X, K)	Returns the indices of K largest entries by magnitude in each row of X
sparse_approximation_rw(X, K)	Keeps only largest K non-zero entries by magnitude in each row of X

Sparse representation matrices (column-wise)

take_along_cols(X, indices)	Picks K entries from each column of X specified by indices matrix
largest_indices_cw(X, K)	Returns the indices of K largest entries by magnitude in each column of X
sparse_approximation_cw(X, K)	Keeps only largest K non-zero entries by magnitude in each column of X

Artificial Noise

awgn_at_snr_ms(key, signal, snr)	Generates noise for the signal at the specified SNR based on signal energy
awgn_at_snr_std(key, signal, snr)	Generates noise for the signal at the specified SNR based on std ratio

Synthetic Signals

pulse	Generates a pulse signal which is 1 between start and end times and 0 everwhere else
transient_sine_wave	Generates a transient sinusoid between start and end times
decaying_sine_wave	Generates a decaying sinusoid :param fs: Sample rate of signal in Hz.
chirp	Generates a frequency sweep from low to high over time.
chirp_centered	Generates a frequency sweep from low to high over time defined by central frequency and bandwidth.
gaussian_pulse	Generates a Gaussian modulated sinusoid
picket_fence	Generates a picket fence signal
heavi_sine	Returns a HeaviSine signal as proposed by Donoho et al. in Wavelab.
bumps	Returns a Bumps signal as proposed by Donoho et al. in Wavelab.
blocks	Returns a Blocks signal as proposed by Donoho et al. in Wavelab.
doppler	Returns a Doppler signal as proposed by Donoho et al. in Wavelab.
ramp	Returns a Ramp signal as proposed by Donoho et al. in Wavelab.
cusp	Returns a Cusp signal as proposed by Donoho et al. in Wavelab.
sing	Returns a Sing signal as proposed by Donoho et al. in Wavelab.
hi_sine	Returns a HiSine signal as proposed by Donoho et al. in Wavelab.
lo_sine	Returns a LoSine signal as proposed by Donoho et al. in Wavelab.
lin_chirp	Returns a LinChirp signal as proposed by Donoho et al. in Wavelab.
two_chirp	Returns a TwoChirp signal as proposed by Donoho et al. in Wavelab.
quad_chirp	Returns a QuadChirp signal as proposed by Donoho et al. in Wavelab.
mish_mash	Returns a MishMash signal as proposed by Donoho et al. in Wavelab.
werner_sorrows	Returns a WernerSorrows signal as proposed by Donoho et al. in Wavelab.
leopold	Returns a Leopold signal as proposed by Donoho et al. in Wavelab.

Discrete Cosine Transform

dct	Computes the 1D Type-II DCT transform
idct	Computes the 1D Type-II Inverse DCT transform
orthonormal_dct	Computes the 1D Type-II DCT transform such that the transform is orthonormal
orthonormal_idct	Computes the 1D Type-II IDCT transform such that the transform is orthonormal

Fast Walsh Hadamard Transform

There is no separate Inverse Fast Walsh Hadamard Transform as FWHT is the inverse of itself except for a normalization factor. In other words, x == fwht(fwht(x)) / n where n is the length of x.

fwht	Computes the Fast Walsh Hadamard Transform over columns

Utilities

time_values

Returns a sequence of time values sampled at a specific frequency for a specific duration