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# 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.

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