# 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. See convolve. convolve2d (in1, in2[, mode, boundary, ...]) Convolve two 2-dimensional arrays. correlate2d (in1, in2[, mode, boundary, ...]) Cross-correlate two 2-dimensional arrays. sepfir2d () sepfir2d(input, hrow, hcol) -> output

## B-splines¶

 bspline (x, n) bspline(x,n): B-spline basis function of order n. uses numpy.piecewise and automatic function-generator. 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 () cspline2d(input {, lambda, precision}) -> ck qspline2d () qspline2d(input {, lambda, precision}) -> qk 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. medfilt2 wiener (im[, mysize, noise]) Perform a Wiener filter on an N-dimensional array. symiirorder1 () symiirorder1(input, c0, z1 {, precision}) -> output symiirorder2 () symiirorder2(input, r, omega {, precision}) -> output lfilter (b, a, x[, axis, zi]) Filter data along one-dimension with an IIR or FIR filter. deconvolve (signal, divisor) Deconvolves divisor out of signal. hilbert (x[, N]) Compute the analytic signal. get_window (window, Nx[, fftbins]) Return a window of length Nx and type window. detrend (data[, axis, type, bp]) Remove linear trend along axis from data. resample (x, num[, t, axis, window]) Resample to num samples using Fourier method along the given axis.

## Filter design¶

 remez (numtaps, bands, desired[, weight, Hz, type, ...]) Calculate the minimax optimal filter using Remez exchange algorithm. firwin (N, cutoff[, width, window]) FIR Filter Design using windowed ideal filter method. iirdesign (wp, ws, gpass, gstop[, analog, ftype, output]) 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. freqs (b, a[, worN, plot]) Compute frequency response of analog filter. freqz (b[, a, worN, whole, ...]) Compute frequency response of a digital filter. unique_roots (p[, tol, rtype]) Determine the unique roots and their multiplicities in two lists 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: r,p,k

## 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 I 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]) Bessel digital and analog filter design.

## Linear Systems¶

 lti Linear Time Invariant class which simplifies representation. lsim (system, U, T[, X0, interp]) Simulate output of a continuous-time linear system. impulse (system[, X0, T, N]) Impulse response of continuous-time system. step (system[, X0, T, N]) Step response of continuous-time system.

## LTI Reresentations¶

 tf2zpk (b, a) Return zero, pole, gain (z,p,k) representation from a numerator, denominator representation of a linear filter. zpk2tf (z, p, k) Return polynomial transfer function representation from zeros and poles tf2ss (num, den) Transfer function to state-space representation. ss2tf (A, B, C, D[, input]) State-space to transfer function. zpk2ss (z, p, k) Zero-pole-gain representation to state-space representation ss2zpk (A, B, C, D[, input]) State-space representation to zero-pole-gain representation.

## Waveforms¶

 sawtooth (t[, width]) Returns a periodic sawtooth waveform with period 2*pi which rises from -1 to 1 on the interval 0 to width*2*pi and drops from 1 to -1 on the interval width*2*pi to 2*pi width must be in the interval [0,1] square (t[, duty]) Returns a periodic square-wave waveform with period 2*pi which is +1 from 0 to 2*pi*duty and -1 from 2*pi*duty to 2*pi duty must be in the interval [0,1] gausspulse (t[, fc, bw, bwr, tpr, ...]) Return a gaussian modulated sinusoid: exp(-a t^2) exp(1j*2*pi*fc) chirp (t[, f0, t1, f1, method, ...]) Frequency-swept cosine generator.

## Window functions¶

 boxcar (M[, sym]) The M-point boxcar window. triang (M[, sym]) The M-point triangular window. parzen (M[, sym]) The M-point Parzen window. bohman (M[, sym]) The M-point Bohman window. blackman (M[, sym]) The M-point Blackman window. blackmanharris (M[, sym]) The M-point minimum 4-term Blackman-Harris window. nuttall (M[, sym]) A minimum 4-term Blackman-Harris window according to Nuttall. flattop (M[, sym]) The M-point Flat top window. bartlett (M[, sym]) The M-point Bartlett window. hann (M[, sym]) The M-point Hanning window. barthann (M[, sym]) Return the M-point modified Bartlett-Hann window. hamming (M[, sym]) The M-point Hamming window. kaiser (M, beta[, sym]) Return a Kaiser window of length M with shape parameter beta. gaussian (M, std[, sym]) Return a Gaussian window of length M with standard-deviation std. general_gaussian (M, p, sig[, sym]) Return a window with a generalized Gaussian shape. slepian (M, width[, sym]) Return the M-point slepian window.

## Wavelets¶

 daub (p) The coefficients for the FIR low-pass filter producing Daubechies wavelets. qmf (hk) Return high-pass qmf filter from low-pass cascade (hk[, J]) (x,phi,psi) at dyadic points K/2**J from filter coefficients.