Signal processing (cupyx.scipy.signal
)#
Convolution#
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Convolve two N-dimensional arrays. |
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Cross-correlate two N-dimensional arrays. |
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Convolve two N-dimensional arrays using FFT. |
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Convolve two N-dimensional arrays using the overlap-add method. |
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Convolve two 2-dimensional arrays. |
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Cross-correlate two 2-dimensional arrays. |
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Convolve with a 2-D separable FIR filter. |
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Find the fastest convolution/correlation method. |
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Calculates the lag / displacement indices array for 1D cross-correlation. |
B-Splines#
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Gaussian approximation to B-spline basis function of order n. |
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Compute cubic spline coefficients for rank-1 array. |
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Compute quadratic spline coefficients for rank-1 array. |
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Coefficients for 2-D cubic (3rd order) B-spline. |
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Coefficients for 2-D quadratic (2nd order) B-spline. |
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Evaluate a cubic spline at the new set of points. |
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Evaluate a quadratic spline at the new set of points. |
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Smoothing spline (cubic) filtering of a rank-2 array. |
Filtering#
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Perform an order filter on an N-D array. |
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Perform a median filter on an N-dimensional array. |
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Median filter a 2-dimensional array. |
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Perform a Wiener filter on an N-dimensional array. |
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Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of first-order sections. The second section uses a reversed sequence. This implements a system with the following transfer function and mirror-symmetric boundary conditions::. |
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Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of second-order sections. The second section uses a reversed sequence. This implements the following transfer function::. |
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Filter data along one-dimension with an IIR or FIR filter. |
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Construct initial conditions for lfilter given input and output vectors. |
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Construct initial conditions for lfilter for step response steady-state. |
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Apply a digital filter forward and backward to a signal. |
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Apply a Savitzky-Golay filter to an array. |
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Deconvolves |
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Filter data along one dimension using cascaded second-order sections. |
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Construct initial conditions for sosfilt for step response steady-state. |
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A forward-backward digital filter using cascaded second-order sections. |
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Compute the analytic signal, using the Hilbert transform. |
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Compute the '2-D' analytic signal of x |
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Downsample the signal after applying an anti-aliasing filter. |
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Remove linear trend along axis from data. |
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Resample x to num samples using Fourier method along the given axis. |
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Resample x along the given axis using polyphase filtering. |
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Upsample, FIR filter, and downsample. |
Filter design#
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Return a digital IIR filter from an analog one using a bilinear transform. |
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Return a digital IIR filter from an analog one using a bilinear transform. |
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Find array of frequencies for computing the response of an analog filter. |
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Compute frequency response of analog filter. |
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Compute frequency response of analog filter. |
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Compute the frequency response of a digital filter. |
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Compute the frequency response of a digital filter in ZPK form. |
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Compute the frequency response of a digital filter in SOS format. |
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FIR filter design using the window method. |
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FIR filter design using the window method. |
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FIR filter design using least-squares error minimization. |
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Convert a linear-phase FIR filter to minimum phase |
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Compute the coefficients for a 1-D Savitzky-Golay FIR filter. |
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Gammatone filter design. |
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Compute the group delay of a digital filter. |
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Complete IIR digital and analog filter design. |
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IIR digital and analog filter design given order and critical points. |
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Compute the attenuation of a Kaiser FIR filter. |
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Compute the Kaiser parameter beta, given the attenuation a. |
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Determine the filter window parameters for the Kaiser window method. |
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Determine unique roots and their multiplicities from a list of roots. |
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Compute partial-fraction expansion of b(s) / a(s). |
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Compute partial-fraction expansion of b(z) / a(z). |
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Compute b(s) and a(s) from partial fraction expansion. |
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Compute b(z) and a(z) from partial fraction expansion. |
Warning about badly conditioned filter coefficients |
Matlab-style IIR filter design#
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Butterworth digital and analog filter design. |
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Butterworth filter order selection. |
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Elliptic (Cauer) digital and analog filter design. |
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Elliptic (Cauer) filter order selection. |
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Chebyshev type I digital and analog filter design. |
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Chebyshev type I filter order selection. |
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Chebyshev type II digital and analog filter design. |
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Chebyshev type II filter order selection. |
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Design IIR notching or peaking digital comb filter. |
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Design second-order IIR notch digital filter. |
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Design second-order IIR peak (resonant) digital filter. |
Low-level filter design functions#
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Check state-space matrices and ensure they are 2-D. |
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Band Stop Objective Function for order minimization. |
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Return (z,p,k) for analog prototype of Nth-order Butterworth filter. |
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Return (z,p,k) for Nth-order Chebyshev type I analog lowpass filter. |
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Return (z,p,k) for Nth-order Chebyshev type I analog lowpass filter. |
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Return (z,p,k) of Nth-order elliptic analog lowpass filter. |
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Transform a lowpass filter prototype to a bandpass filter. |
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Transform a lowpass filter prototype to a bandpass filter. |
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Transform a lowpass filter prototype to a bandstop filter. |
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Transform a lowpass filter prototype to a bandstop filter. |
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Transform a lowpass filter prototype to a highpass filter. |
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Transform a lowpass filter prototype to a highpass filter. |
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Transform a lowpass filter prototype to a different frequency. |
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Transform a lowpass filter prototype to a different frequency. |
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Normalize numerator/denominator of a continuous-time transfer function. |
LTI representations#
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Return polynomial transfer function representation from zeros and poles |
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Return second-order sections from zeros, poles, and gain of a system |
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Zero-pole-gain representation to state-space representation |
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Return zero, pole, gain (z, p, k) representation from a numerator, denominator representation of a linear filter. |
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Return second-order sections from transfer function representation |
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Transfer function to state-space representation. |
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State-space to transfer function. |
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State-space representation to zero-pole-gain representation. |
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Return a single transfer function from a series of second-order sections |
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Return zeros, poles, and gain of a series of second-order sections |
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Transform a continuous to a discrete state-space system. |
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Compute K such that eigenvalues (A - dot(B, K))=poles. |
Continuous-time linear systems#
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Continuous-time linear time invariant system base class. |
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Linear Time Invariant system in state-space form. |
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Linear Time Invariant system class in transfer function form. |
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Linear Time Invariant system class in zeros, poles, gain form. |
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Simulate output of a continuous-time linear system. |
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Impulse response of continuous-time system. |
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Step response of continuous-time system. |
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Calculate the frequency response of a continuous-time system. |
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Calculate Bode magnitude and phase data of a continuous-time system. |
Discrete-time linear systems#
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Discrete-time linear time invariant system base class. |
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Linear Time Invariant system in state-space form. |
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Linear Time Invariant system class in transfer function form. |
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Linear Time Invariant system class in zeros, poles, gain form. |
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Simulate output of a discrete-time linear system. |
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Impulse response of discrete-time system. |
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Step response of discrete-time system. |
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Calculate the frequency response of a discrete-time system. |
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Calculate Bode magnitude and phase data of a discrete-time system. |
Waveforms#
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Frequency-swept cosine generator. |
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Return a Gaussian modulated sinusoid: |
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Maximum length sequence (MLS) generator. |
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Return a periodic sawtooth or triangle waveform. |
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Return a periodic square-wave waveform. |
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Unit impulse signal (discrete delta function) or unit basis vector. |
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Frequency-swept cosine generator, with a time-dependent frequency. |
Window functions#
For window functions, see the cupyx.scipy.signal.windows
namespace.
In the cupyx.scipy.signal
namespace, there is a convenience function
to obtain these windows by name:
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Return a window of a given length and type. |
Wavelets#
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Complex Morlet wavelet. |
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Return high-pass qmf filter from low-pass |
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Return a Ricker wavelet, also known as the "Mexican hat wavelet". |
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Complex Morlet wavelet, designed to work with cwt. Returns the complete version of morlet wavelet, normalised according to s::. |
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Continuous wavelet transform. |
Peak finding#
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Calculate the relative minima of data. |
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Calculate the relative maxima of data. |
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Calculate the relative extrema of data. |
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Find peaks inside a signal based on peak properties. |
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Calculate the prominence of each peak in a signal. |
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Calculate the width of each peak in a signal. |
Spectral analysis#
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Estimate power spectral density using a periodogram. |
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Estimate power spectral density using Welch's method. |
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Estimate the cross power spectral density, Pxy, using Welch's method. |
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Estimate the magnitude squared coherence estimate, Cxy, of discrete-time signals X and Y using Welch's method. |
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Compute a spectrogram with consecutive Fourier transforms. |
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Computes the Lomb-Scargle periodogram. |
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Determine the vector strength of the events corresponding to the given period. |
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Compute the Short Time Fourier Transform (STFT). |
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Perform the inverse Short Time Fourier transform (iSTFT). |
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Check whether the Constant OverLap Add (COLA) constraint is met. |
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Check whether the Nonzero Overlap Add (NOLA) constraint is met. |
Chirp Z-transform and Zoom FFT#
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Compute the frequency response around a spiral in the Z plane. |
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Compute the DFT of x only for frequencies in range fn. |
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Create a callable chirp z-transform function. |
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Create a callable zoom FFT transform function. |
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Return the points at which the chirp z-transform is computed. |