Signal processing--scipy.signal

本文全面介绍了信号处理领域的核心概念和技术,包括卷积、相关运算、滤波器设计、连续及离散时间系统的分析等。此外,还详细阐述了各类窗函数、波形生成方法以及峰值检测算法等内容。

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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.
BadCoefficientsWarning 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
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