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]) | 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: |
choose_conv_method (in1, in2[, mode, measure]) | Find the fastest convolution/correlation method. |
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 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]) | 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[, 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]) | Compute the frequency response of a digital filter. |
freqz_zpk (z, p, k[, worN, whole]) | Compute the frequency response of a digital filter in ZPK form. |
sosfreqz (sos[, worN, whole]) | Compute the frequency response of a digital filter in SOS format. |
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) | 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 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 numerator/denominator of a continuous-time 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. |
iirnotch (w0, Q) | Design second-order IIR notch digital filter. |
iirpeak (w0, Q) | Design second-order IIR peak (resonant) digital 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
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. |
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 |