Signal processing (scipy.signal)

Convolution

convolve(in1, in2[, mode, method])	Convolve two N-dimensional arrays.
correlate(in1, in2[, mode, method])	Cross-correlate two N-dimensional arrays.
fftconvolve(in1, in2[, mode, axes])	Convolve two N-dimensional arrays using FFT.
oaconvolve(in1, in2[, mode, axes])	Convolve two N-dimensional arrays using the overlap-add method.
convolve2d(in1, in2[, mode, boundary, fillvalue])	Convolve two 2-dimensional arrays.
correlate2d(in1, in2[, mode, boundary, …])	Cross-correlate two 2-dimensional arrays.
sepfir2d(input, hrow, hcol)	Convolve with a 2-D separable FIR filter.
choose_conv_method(in1, in2[, mode, measure])	Find the fastest convolution/correlation method.
correlation_lags(in1_len, in2_len[, mode])	Calculates the lag / displacement indices array for 1D cross-correlation.

B-splines

bspline(x, n)	B-spline basis function of order n.
cubic(x)	A cubic B-spline.
quadratic(x)	A quadratic B-spline.
gauss_spline(x, n)	Gaussian approximation to B-spline basis function of order n.
cspline1d(signal[, lamb])	Compute cubic spline coefficients for rank-1 array.
qspline1d(signal[, lamb])	Compute quadratic spline coefficients for rank-1 array.
cspline2d(input[, lambda, precision])	Coefficients for 2-D cubic (3rd order) B-spline.
qspline2d(input[, lambda, precision])	Coefficients for 2-D quadratic (2nd order) B-spline:
cspline1d_eval(cj, newx[, dx, x0])	Evaluate a cubic spline at the new set of points.
qspline1d_eval(cj, newx[, dx, x0])	Evaluate a quadratic spline at the new set of points.
spline_filter(Iin[, lmbda])	Smoothing spline (cubic) filtering of a rank-2 array.

Filtering

order_filter(a, domain, rank)	Perform an order filter on an N-D array.
medfilt(volume[, kernel_size])	Perform a median filter on an N-dimensional array.
medfilt2d(input[, kernel_size])	Median filter a 2-dimensional array.
wiener(im[, mysize, noise])	Perform a Wiener filter on an N-dimensional array.
symiirorder1(input, c0, z1[, precision])	Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of first-order sections.
symiirorder2(input, r, omega[, precision])	Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of second-order sections.
lfilter(b, a, x[, axis, zi])	Filter data along one-dimension with an IIR or FIR filter.
lfiltic(b, a, y[, x])	Construct initial conditions for lfilter given input and output vectors.
lfilter_zi(b, a)	Construct initial conditions for lfilter for step response steady-state.
filtfilt(b, a, x[, axis, padtype, padlen, …])	Apply a digital filter forward and backward to a signal.
savgol_filter(x, window_length, polyorder[, …])	Apply a Savitzky-Golay filter to an array.
deconvolve(signal, divisor)	Deconvolves divisor out of signal using inverse filtering.
sosfilt(sos, x[, axis, zi])	Filter data along one dimension using cascaded second-order sections.
sosfilt_zi(sos)	Construct initial conditions for sosfilt for step response steady-state.
sosfiltfilt(sos, x[, axis, padtype, padlen])	A forward-backward digital filter using cascaded second-order sections.
hilbert(x[, N, axis])	Compute the analytic signal, using the Hilbert transform.
hilbert2(x[, N])	Compute the ‘2-D’ analytic signal of x
decimate(x, q[, n, ftype, axis, zero_phase])	Downsample the signal after applying an anti-aliasing filter.
detrend(data[, axis, type, bp, overwrite_data])	Remove linear trend along axis from data.
resample(x, num[, t, axis, window, domain])	Resample x to num samples using Fourier method along the given axis.
resample_poly(x, up, down[, axis, window, …])	Resample x along the given axis using polyphase filtering.
upfirdn(h, x[, up, down, axis, mode, cval])	Upsample, FIR filter, and downsample.

Filter design

bilinear(b, a[, fs])	Return a digital IIR filter from an analog one using a bilinear transform.
bilinear_zpk(z, p, k, fs)	Return a digital IIR filter from an analog one using a bilinear transform.
findfreqs(num, den, N[, kind])	Find array of frequencies for computing the response of an analog filter.
firls(numtaps, bands, desired[, weight, nyq, fs])	FIR filter design using least-squares error minimization.
firwin(numtaps, cutoff[, width, window, …])	FIR filter design using the window method.
firwin2(numtaps, freq, gain[, nfreqs, …])	FIR filter design using the window method.
freqs(b, a[, worN, plot])	Compute frequency response of analog filter.
freqs_zpk(z, p, k[, worN])	Compute frequency response of analog filter.
freqz(b[, a, worN, whole, plot, fs, …])	Compute the frequency response of a digital filter.
freqz_zpk(z, p, k[, worN, whole, fs])	Compute the frequency response of a digital filter in ZPK form.
sosfreqz(sos[, worN, whole, fs])	Compute the frequency response of a digital filter in SOS format.
gammatone(freq, ftype[, order, numtaps, fs])	Gammatone filter design.
group_delay(system[, w, whole, fs])	Compute the group delay of a digital filter.
iirdesign(wp, ws, gpass, gstop[, analog, …])	Complete IIR digital and analog filter design.
iirfilter(N, Wn[, rp, rs, btype, analog, …])	IIR digital and analog filter design given order and critical points.
kaiser_atten(numtaps, width)	Compute the attenuation of a Kaiser FIR filter.
kaiser_beta(a)	Compute the Kaiser parameter beta, given the attenuation a.
kaiserord(ripple, width)	Determine the filter window parameters for the Kaiser window method.
minimum_phase(h[, method, n_fft])	Convert a linear-phase FIR filter to minimum phase
savgol_coeffs(window_length, polyorder[, …])	Compute the coefficients for a 1-D Savitzky-Golay FIR filter.
remez(numtaps, bands, desired[, weight, Hz, …])	Calculate the minimax optimal filter using the Remez exchange algorithm.
unique_roots(p[, tol, rtype])	Determine unique roots and their multiplicities from a list of roots.
residue(b, a[, tol, rtype])	Compute partial-fraction expansion of b(s) / a(s).
residuez(b, a[, tol, rtype])	Compute partial-fraction expansion of b(z) / a(z).
invres(r, p, k[, tol, rtype])	Compute b(s) and a(s) from partial fraction expansion.
invresz(r, p, k[, tol, rtype])	Compute b(z) and a(z) from partial fraction expansion.
BadCoefficients	Warning about badly conditioned filter coefficients

Lower-level filter design functions:

abcd_normalize([A, B, C, D])	Check state-space matrices and ensure they are 2-D.
band_stop_obj(wp, ind, passb, stopb, gpass, …)	Band Stop Objective Function for order minimization.
besselap(N[, norm])	Return (z,p,k) for analog prototype of an Nth-order Bessel filter.
buttap(N)	Return (z,p,k) for analog prototype of Nth-order Butterworth filter.
cheb1ap(N, rp)	Return (z,p,k) for Nth-order Chebyshev type I analog lowpass filter.
cheb2ap(N, rs)	Return (z,p,k) for Nth-order Chebyshev type I analog lowpass filter.
cmplx_sort(p)	Sort roots based on magnitude.
ellipap(N, rp, rs)	Return (z,p,k) of Nth-order elliptic analog lowpass filter.
lp2bp(b, a[, wo, bw])	Transform a lowpass filter prototype to a bandpass filter.
lp2bp_zpk(z, p, k[, wo, bw])	Transform a lowpass filter prototype to a bandpass filter.
lp2bs(b, a[, wo, bw])	Transform a lowpass filter prototype to a bandstop filter.
lp2bs_zpk(z, p, k[, wo, bw])	Transform a lowpass filter prototype to a bandstop filter.
lp2hp(b, a[, wo])	Transform a lowpass filter prototype to a highpass filter.
lp2hp_zpk(z, p, k[, wo])	Transform a lowpass filter prototype to a highpass filter.
lp2lp(b, a[, wo])	Transform a lowpass filter prototype to a different frequency.
lp2lp_zpk(z, p, k[, wo])	Transform a lowpass filter prototype to a different frequency.
normalize(b, a)	Normalize numerator/denominator of a continuous-time transfer function.

Matlab-style IIR filter design

butter(N, Wn[, btype, analog, output, fs])	Butterworth digital and analog filter design.
buttord(wp, ws, gpass, gstop[, analog, fs])	Butterworth filter order selection.
cheby1(N, rp, Wn[, btype, analog, output, fs])	Chebyshev type I digital and analog filter design.
cheb1ord(wp, ws, gpass, gstop[, analog, fs])	Chebyshev type I filter order selection.
cheby2(N, rs, Wn[, btype, analog, output, fs])	Chebyshev type II digital and analog filter design.
cheb2ord(wp, ws, gpass, gstop[, analog, fs])	Chebyshev type II filter order selection.
ellip(N, rp, rs, Wn[, btype, analog, output, fs])	Elliptic (Cauer) digital and analog filter design.
ellipord(wp, ws, gpass, gstop[, analog, fs])	Elliptic (Cauer) filter order selection.
bessel(N, Wn[, btype, analog, output, norm, fs])	Bessel/Thomson digital and analog filter design.
iirnotch(w0, Q[, fs])	Design second-order IIR notch digital filter.
iirpeak(w0, Q[, fs])	Design second-order IIR peak (resonant) digital filter.
iircomb(w0, Q[, ftype, fs])	Design IIR notching or peaking digital comb filter.

Continuous-time linear systems

lti(*system)	Continuous-time linear time invariant system base class.
StateSpace(*system, **kwargs)	Linear Time Invariant system in state-space form.
TransferFunction(*system, **kwargs)	Linear Time Invariant system class in transfer function form.
ZerosPolesGain(*system, **kwargs)	Linear Time Invariant system class in zeros, poles, gain form.
lsim(system, U, T[, X0, interp])	Simulate output of a continuous-time linear system.
lsim2(system[, U, T, X0])	Simulate output of a continuous-time linear system, by using the ODE solver scipy.integrate.odeint.
impulse(system[, X0, T, N])	Impulse response of continuous-time system.
impulse2(system[, X0, T, N])	Impulse response of a single-input, continuous-time linear system.
step(system[, X0, T, N])	Step response of continuous-time system.
step2(system[, X0, T, N])	Step response of continuous-time system.
freqresp(system[, w, n])	Calculate the frequency response of a continuous-time system.
bode(system[, w, n])	Calculate Bode magnitude and phase data of a continuous-time system.

Discrete-time linear systems

dlti(*system, **kwargs)	Discrete-time linear time invariant system base class.
StateSpace(*system, **kwargs)	Linear Time Invariant system in state-space form.
TransferFunction(*system, **kwargs)	Linear Time Invariant system class in transfer function form.
ZerosPolesGain(*system, **kwargs)	Linear Time Invariant system class in zeros, poles, gain form.
dlsim(system, u[, t, x0])	Simulate output of a discrete-time linear system.
dimpulse(system[, x0, t, n])	Impulse response of discrete-time system.
dstep(system[, x0, t, n])	Step response of discrete-time system.
dfreqresp(system[, w, n, whole])	Calculate the frequency response of a discrete-time system.
dbode(system[, w, n])	Calculate Bode magnitude and phase data of a discrete-time system.

LTI representations

tf2zpk(b, a)	Return zero, pole, gain (z, p, k) representation from a numerator, denominator representation of a linear filter.
tf2sos(b, a[, pairing])	Return second-order sections from transfer function representation
tf2ss(num, den)	Transfer function to state-space representation.
zpk2tf(z, p, k)	Return polynomial transfer function representation from zeros and poles
zpk2sos(z, p, k[, pairing])	Return second-order sections from zeros, poles, and gain of a system
zpk2ss(z, p, k)	Zero-pole-gain representation to state-space representation
ss2tf(A, B, C, D[, input])	State-space to transfer function.
ss2zpk(A, B, C, D[, input])	State-space representation to zero-pole-gain representation.
sos2zpk(sos)	Return zeros, poles, and gain of a series of second-order sections
sos2tf(sos)	Return a single transfer function from a series of second-order sections
cont2discrete(system, dt[, method, alpha])	Transform a continuous to a discrete state-space system.
place_poles(A, B, poles[, method, rtol, maxiter])	Compute K such that eigenvalues (A - dot(B, K))=poles.

Waveforms

chirp(t, f0, t1, f1[, method, phi, vertex_zero])	Frequency-swept cosine generator.
gausspulse(t[, fc, bw, bwr, tpr, retquad, …])	Return a Gaussian modulated sinusoid:
max_len_seq(nbits[, state, length, taps])	Maximum length sequence (MLS) generator.
sawtooth(t[, width])	Return a periodic sawtooth or triangle waveform.
square(t[, duty])	Return a periodic square-wave waveform.
sweep_poly(t, poly[, phi])	Frequency-swept cosine generator, with a time-dependent frequency.
unit_impulse(shape[, idx, dtype])	Unit impulse signal (discrete delta function) or unit basis vector.

Window functions

For window functions, see the scipy.signal.windows namespace.

In the scipy.signal namespace, there is a convenience function to obtain these windows by name:

get_window(window, Nx[, fftbins])

Return a window of a given length and type.

Wavelets

cascade(hk[, J])	Return (x, phi, psi) at dyadic points K/2**J from filter coefficients.
daub(p)	The coefficients for the FIR low-pass filter producing Daubechies wavelets.
morlet(M[, w, s, complete])	Complex Morlet wavelet.
qmf(hk)	Return high-pass qmf filter from low-pass
ricker(points, a)	Return a Ricker wavelet, also known as the “Mexican hat wavelet”.
morlet2(M, s[, w])	Complex Morlet wavelet, designed to work with cwt.
cwt(data, wavelet, widths[, dtype])	Continuous wavelet transform.

Peak finding

argrelmin(data[, axis, order, mode])	Calculate the relative minima of data.
argrelmax(data[, axis, order, mode])	Calculate the relative maxima of data.
argrelextrema(data, comparator[, axis, …])	Calculate the relative extrema of data.
find_peaks(x[, height, threshold, distance, …])	Find peaks inside a signal based on peak properties.
find_peaks_cwt(vector, widths[, wavelet, …])	Find peaks in a 1-D array with wavelet transformation.
peak_prominences(x, peaks[, wlen])	Calculate the prominence of each peak in a signal.
peak_widths(x, peaks[, rel_height, …])	Calculate the width of each peak in a signal.

Spectral analysis

periodogram(x[, fs, window, nfft, detrend, …])	Estimate power spectral density using a periodogram.
welch(x[, fs, window, nperseg, noverlap, …])	Estimate power spectral density using Welch’s method.
csd(x, y[, fs, window, nperseg, noverlap, …])	Estimate the cross power spectral density, Pxy, using Welch’s method.
coherence(x, y[, fs, window, nperseg, …])	Estimate the magnitude squared coherence estimate, Cxy, of discrete-time signals X and Y using Welch’s method.
spectrogram(x[, fs, window, nperseg, …])	Compute a spectrogram with consecutive Fourier transforms.
lombscargle(x, y, freqs)	Computes the Lomb-Scargle periodogram.
vectorstrength(events, period)	Determine the vector strength of the events corresponding to the given period.
stft(x[, fs, window, nperseg, noverlap, …])	Compute the Short Time Fourier Transform (STFT).
istft(Zxx[, fs, window, nperseg, noverlap, …])	Perform the inverse Short Time Fourier transform (iSTFT).
check_COLA(window, nperseg, noverlap[, tol])	Check whether the Constant OverLap Add (COLA) constraint is met
check_NOLA(window, nperseg, noverlap[, tol])	Check whether the Nonzero Overlap Add (NOLA) constraint is met