SciPy

Signal processing (scipy.signal)

Convolution

convolve(in1, in2[, mode]) Convolve two N-dimensional arrays.
correlate(in1, in2[, mode]) Cross-correlate two N-dimensional arrays.
fftconvolve(in1, in2[, mode]) Convolve two N-dimensional arrays using FFT.
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) -> output) Description:

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}) -> ck) Description:
qspline2d((input {, lambda, precision}) -> qk) Description:
cspline1d_eval(cj, newx[, dx, x0]) Evaluate a 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-dimensional 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 {, ...) Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of first-order sections.
symiirorder2((input, r, omega {, ...) 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.
lfilter_zi(b, a) Compute an initial state zi for the lfilter function that corresponds to the steady state of the step response.
filtfilt(b, a, x[, axis, padtype, padlen, ...]) A forward-backward filter.
savgol_filter(x, window_length, polyorder[, ...]) Apply a Savitzky-Golay filter to an array.
deconvolve(signal, divisor) Deconvolves divisor out of signal.
sosfilt(sos, x[, axis, zi]) Filter data along one dimension using cascaded second-order sections
sosfilt_zi(sos) Compute an initial state zi for the sosfilt function that corresponds to the steady state of the step response.
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]) Remove linear trend along axis from data.
resample(x, num[, t, axis, window]) 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]) Upsample, FIR filter, and downsample

Filter design

bilinear(b, a[, fs]) Return a digital filter from an analog one using a bilinear transform.
findfreqs(num, den, N) Find array of frequencies for computing the response of an analog filter.
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.
freqz(b[, a, worN, whole, plot]) Compute the frequency response of a digital filter.
group_delay(system[, w, whole]) 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) Design a Kaiser window to limit ripple and width of transition region.
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 two-dimensional.
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.
lp2bs(b, a[, wo, bw]) Transform a lowpass filter prototype to a bandstop filter.
lp2hp(b, a[, wo]) Transform a lowpass filter prototype to a highpass filter.
lp2lp(b, a[, wo]) Transform a lowpass filter prototype to a different frequency.
normalize(b, a) Normalize polynomial representation of a transfer function.

Matlab-style IIR filter design

butter(N, Wn[, btype, analog, output]) Butterworth digital and analog filter design.
buttord(wp, ws, gpass, gstop[, analog]) Butterworth filter order selection.
cheby1(N, rp, Wn[, btype, analog, output]) Chebyshev type I digital and analog filter design.
cheb1ord(wp, ws, gpass, gstop[, analog]) Chebyshev type I filter order selection.
cheby2(N, rs, Wn[, btype, analog, output]) Chebyshev type II digital and analog filter design.
cheb2ord(wp, ws, gpass, gstop[, analog]) Chebyshev type II filter order selection.
ellip(N, rp, rs, Wn[, btype, analog, output]) Elliptic (Cauer) digital and analog filter design.
ellipord(wp, ws, gpass, gstop[, analog]) Elliptic (Cauer) filter order selection.
bessel(N, Wn[, btype, analog, output, norm]) Bessel/Thomson digital and analog filter design.

Continuous-Time Linear Systems

freqresp(system[, w, n]) Calculate the frequency response of a continuous-time system.
lti(*system) Linear Time Invariant system base class.
StateSpace(*system) Linear Time Invariant system class in state-space form.
TransferFunction(*system) Linear Time Invariant system class in transfer function form.
ZerosPolesGain(*system) 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.
bode(system[, w, n]) Calculate Bode magnitude and phase data of a continuous-time system.

Discrete-Time Linear Systems

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.

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(sys, 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.

Window functions

get_window(window, Nx[, fftbins]) Return a window.
barthann(M[, sym]) Return a modified Bartlett-Hann window.
bartlett(M[, sym]) Return a Bartlett window.
blackman(M[, sym]) Return a Blackman window.
blackmanharris(M[, sym]) Return a minimum 4-term Blackman-Harris window.
bohman(M[, sym]) Return a Bohman window.
boxcar(M[, sym]) Return a boxcar or rectangular window.
chebwin(M, at[, sym]) Return a Dolph-Chebyshev window.
cosine(M[, sym]) Return a window with a simple cosine shape.
exponential(M[, center, tau, sym]) Return an exponential (or Poisson) window.
flattop(M[, sym]) Return a flat top window.
gaussian(M, std[, sym]) Return a Gaussian window.
general_gaussian(M, p, sig[, sym]) Return a window with a generalized Gaussian shape.
hamming(M[, sym]) Return a Hamming window.
hann(M[, sym]) Return a Hann window.
hanning(M[, sym]) Return a Hann window.
kaiser(M, beta[, sym]) Return a Kaiser window.
nuttall(M[, sym]) Return a minimum 4-term Blackman-Harris window according to Nuttall.
parzen(M[, sym]) Return a Parzen window.
slepian(M, width[, sym]) Return a digital Slepian (DPSS) window.
triang(M[, sym]) Return a triangular window.
tukey(M[, alpha, sym]) Return a Tukey window, also known as a tapered cosine window.

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”.
cwt(data, wavelet, widths) Continuous wavelet transform.

Peak finding

find_peaks_cwt(vector, widths[, wavelet, ...]) Attempt to find the peaks in a 1-D array.
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.

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.