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365 lines
14 KiB
Python
365 lines
14 KiB
Python
"""
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=======================================
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Signal processing (:mod:`scipy.signal`)
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=======================================
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Convolution
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===========
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.. autosummary::
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:toctree: generated/
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convolve -- N-D convolution.
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correlate -- N-D correlation.
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fftconvolve -- N-D convolution using the FFT.
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oaconvolve -- N-D convolution using the overlap-add method.
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convolve2d -- 2-D convolution (more options).
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correlate2d -- 2-D correlation (more options).
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sepfir2d -- Convolve with a 2-D separable FIR filter.
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choose_conv_method -- Chooses faster of FFT and direct convolution methods.
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correlation_lags -- Determines lag indices for 1D cross-correlation.
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B-splines
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=========
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.. autosummary::
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:toctree: generated/
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bspline -- B-spline basis function of order n.
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cubic -- B-spline basis function of order 3.
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quadratic -- B-spline basis function of order 2.
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gauss_spline -- Gaussian approximation to the B-spline basis function.
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cspline1d -- Coefficients for 1-D cubic (3rd order) B-spline.
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qspline1d -- Coefficients for 1-D quadratic (2nd order) B-spline.
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cspline2d -- Coefficients for 2-D cubic (3rd order) B-spline.
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qspline2d -- Coefficients for 2-D quadratic (2nd order) B-spline.
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cspline1d_eval -- Evaluate a cubic spline at the given points.
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qspline1d_eval -- Evaluate a quadratic spline at the given points.
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spline_filter -- Smoothing spline (cubic) filtering of a rank-2 array.
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Filtering
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=========
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.. autosummary::
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:toctree: generated/
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order_filter -- N-D order filter.
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medfilt -- N-D median filter.
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medfilt2d -- 2-D median filter (faster).
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wiener -- N-D Wiener filter.
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symiirorder1 -- 2nd-order IIR filter (cascade of first-order systems).
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symiirorder2 -- 4th-order IIR filter (cascade of second-order systems).
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lfilter -- 1-D FIR and IIR digital linear filtering.
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lfiltic -- Construct initial conditions for `lfilter`.
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lfilter_zi -- Compute an initial state zi for the lfilter function that
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-- corresponds to the steady state of the step response.
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filtfilt -- A forward-backward filter.
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savgol_filter -- Filter a signal using the Savitzky-Golay filter.
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deconvolve -- 1-D deconvolution using lfilter.
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sosfilt -- 1-D IIR digital linear filtering using
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-- a second-order sections filter representation.
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sosfilt_zi -- Compute an initial state zi for the sosfilt function that
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-- corresponds to the steady state of the step response.
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sosfiltfilt -- A forward-backward filter for second-order sections.
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hilbert -- Compute 1-D analytic signal, using the Hilbert transform.
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hilbert2 -- Compute 2-D analytic signal, using the Hilbert transform.
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decimate -- Downsample a signal.
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detrend -- Remove linear and/or constant trends from data.
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resample -- Resample using Fourier method.
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resample_poly -- Resample using polyphase filtering method.
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upfirdn -- Upsample, apply FIR filter, downsample.
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Filter design
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=============
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.. autosummary::
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:toctree: generated/
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bilinear -- Digital filter from an analog filter using
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-- the bilinear transform.
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bilinear_zpk -- Digital filter from an analog filter using
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-- the bilinear transform.
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findfreqs -- Find array of frequencies for computing filter response.
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firls -- FIR filter design using least-squares error minimization.
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firwin -- Windowed FIR filter design, with frequency response
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-- defined as pass and stop bands.
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firwin2 -- Windowed FIR filter design, with arbitrary frequency
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-- response.
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freqs -- Analog filter frequency response from TF coefficients.
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freqs_zpk -- Analog filter frequency response from ZPK coefficients.
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freqz -- Digital filter frequency response from TF coefficients.
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freqz_zpk -- Digital filter frequency response from ZPK coefficients.
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sosfreqz -- Digital filter frequency response for SOS format filter.
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gammatone -- FIR and IIR gammatone filter design.
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group_delay -- Digital filter group delay.
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iirdesign -- IIR filter design given bands and gains.
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iirfilter -- IIR filter design given order and critical frequencies.
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kaiser_atten -- Compute the attenuation of a Kaiser FIR filter, given
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-- the number of taps and the transition width at
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-- discontinuities in the frequency response.
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kaiser_beta -- Compute the Kaiser parameter beta, given the desired
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-- FIR filter attenuation.
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kaiserord -- Design a Kaiser window to limit ripple and width of
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-- transition region.
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minimum_phase -- Convert a linear phase FIR filter to minimum phase.
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savgol_coeffs -- Compute the FIR filter coefficients for a Savitzky-Golay
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-- filter.
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remez -- Optimal FIR filter design.
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unique_roots -- Unique roots and their multiplicities.
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residue -- Partial fraction expansion of b(s) / a(s).
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residuez -- Partial fraction expansion of b(z) / a(z).
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invres -- Inverse partial fraction expansion for analog filter.
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invresz -- Inverse partial fraction expansion for digital filter.
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BadCoefficients -- Warning on badly conditioned filter coefficients.
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Lower-level filter design functions:
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.. autosummary::
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:toctree: generated/
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abcd_normalize -- Check state-space matrices and ensure they are rank-2.
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band_stop_obj -- Band Stop Objective Function for order minimization.
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besselap -- Return (z,p,k) for analog prototype of Bessel filter.
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buttap -- Return (z,p,k) for analog prototype of Butterworth filter.
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cheb1ap -- Return (z,p,k) for type I Chebyshev filter.
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cheb2ap -- Return (z,p,k) for type II Chebyshev filter.
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cmplx_sort -- Sort roots based on magnitude.
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ellipap -- Return (z,p,k) for analog prototype of elliptic filter.
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lp2bp -- Transform a lowpass filter prototype to a bandpass filter.
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lp2bp_zpk -- Transform a lowpass filter prototype to a bandpass filter.
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lp2bs -- Transform a lowpass filter prototype to a bandstop filter.
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lp2bs_zpk -- Transform a lowpass filter prototype to a bandstop filter.
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lp2hp -- Transform a lowpass filter prototype to a highpass filter.
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lp2hp_zpk -- Transform a lowpass filter prototype to a highpass filter.
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lp2lp -- Transform a lowpass filter prototype to a lowpass filter.
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lp2lp_zpk -- Transform a lowpass filter prototype to a lowpass filter.
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normalize -- Normalize polynomial representation of a transfer function.
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Matlab-style IIR filter design
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==============================
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.. autosummary::
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:toctree: generated/
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butter -- Butterworth
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buttord
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cheby1 -- Chebyshev Type I
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cheb1ord
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cheby2 -- Chebyshev Type II
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cheb2ord
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ellip -- Elliptic (Cauer)
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ellipord
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bessel -- Bessel (no order selection available -- try butterod)
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iirnotch -- Design second-order IIR notch digital filter.
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iirpeak -- Design second-order IIR peak (resonant) digital filter.
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iircomb -- Design IIR comb filter.
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Continuous-time linear systems
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==============================
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.. autosummary::
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:toctree: generated/
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lti -- Continuous-time linear time invariant system base class.
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StateSpace -- Linear time invariant system in state space form.
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TransferFunction -- Linear time invariant system in transfer function form.
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ZerosPolesGain -- Linear time invariant system in zeros, poles, gain form.
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lsim -- Continuous-time simulation of output to linear system.
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lsim2 -- Like lsim, but `scipy.integrate.odeint` is used.
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impulse -- Impulse response of linear, time-invariant (LTI) system.
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impulse2 -- Like impulse, but `scipy.integrate.odeint` is used.
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step -- Step response of continuous-time LTI system.
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step2 -- Like step, but `scipy.integrate.odeint` is used.
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freqresp -- Frequency response of a continuous-time LTI system.
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bode -- Bode magnitude and phase data (continuous-time LTI).
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Discrete-time linear systems
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============================
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.. autosummary::
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:toctree: generated/
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dlti -- Discrete-time linear time invariant system base class.
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StateSpace -- Linear time invariant system in state space form.
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TransferFunction -- Linear time invariant system in transfer function form.
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ZerosPolesGain -- Linear time invariant system in zeros, poles, gain form.
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dlsim -- Simulation of output to a discrete-time linear system.
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dimpulse -- Impulse response of a discrete-time LTI system.
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dstep -- Step response of a discrete-time LTI system.
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dfreqresp -- Frequency response of a discrete-time LTI system.
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dbode -- Bode magnitude and phase data (discrete-time LTI).
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LTI representations
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===================
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.. autosummary::
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:toctree: generated/
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tf2zpk -- Transfer function to zero-pole-gain.
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tf2sos -- Transfer function to second-order sections.
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tf2ss -- Transfer function to state-space.
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zpk2tf -- Zero-pole-gain to transfer function.
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zpk2sos -- Zero-pole-gain to second-order sections.
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zpk2ss -- Zero-pole-gain to state-space.
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ss2tf -- State-pace to transfer function.
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ss2zpk -- State-space to pole-zero-gain.
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sos2zpk -- Second-order sections to zero-pole-gain.
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sos2tf -- Second-order sections to transfer function.
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cont2discrete -- Continuous-time to discrete-time LTI conversion.
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place_poles -- Pole placement.
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Waveforms
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=========
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.. autosummary::
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:toctree: generated/
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chirp -- Frequency swept cosine signal, with several freq functions.
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gausspulse -- Gaussian modulated sinusoid.
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max_len_seq -- Maximum length sequence.
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sawtooth -- Periodic sawtooth.
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square -- Square wave.
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sweep_poly -- Frequency swept cosine signal; freq is arbitrary polynomial.
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unit_impulse -- Discrete unit impulse.
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Window functions
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================
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For window functions, see the `scipy.signal.windows` namespace.
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In the `scipy.signal` namespace, there is a convenience function to
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obtain these windows by name:
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.. autosummary::
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:toctree: generated/
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get_window -- Return a window of a given length and type.
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Wavelets
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========
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.. autosummary::
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:toctree: generated/
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cascade -- Compute scaling function and wavelet from coefficients.
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daub -- Return low-pass.
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morlet -- Complex Morlet wavelet.
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qmf -- Return quadrature mirror filter from low-pass.
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ricker -- Return ricker wavelet.
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morlet2 -- Return Morlet wavelet, compatible with cwt.
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cwt -- Perform continuous wavelet transform.
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Peak finding
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============
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.. autosummary::
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:toctree: generated/
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argrelmin -- Calculate the relative minima of data.
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argrelmax -- Calculate the relative maxima of data.
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argrelextrema -- Calculate the relative extrema of data.
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find_peaks -- Find a subset of peaks inside a signal.
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find_peaks_cwt -- Find peaks in a 1-D array with wavelet transformation.
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peak_prominences -- Calculate the prominence of each peak in a signal.
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peak_widths -- Calculate the width of each peak in a signal.
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Spectral analysis
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=================
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.. autosummary::
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:toctree: generated/
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periodogram -- Compute a (modified) periodogram.
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welch -- Compute a periodogram using Welch's method.
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csd -- Compute the cross spectral density, using Welch's method.
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coherence -- Compute the magnitude squared coherence, using Welch's method.
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spectrogram -- Compute the spectrogram.
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lombscargle -- Computes the Lomb-Scargle periodogram.
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vectorstrength -- Computes the vector strength.
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stft -- Compute the Short Time Fourier Transform.
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istft -- Compute the Inverse Short Time Fourier Transform.
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check_COLA -- Check the COLA constraint for iSTFT reconstruction.
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check_NOLA -- Check the NOLA constraint for iSTFT reconstruction.
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"""
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from . import sigtools, windows
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from .waveforms import *
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from ._max_len_seq import max_len_seq
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from ._upfirdn import upfirdn
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# The spline module (a C extension) provides:
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# cspline2d, qspline2d, sepfir2d, symiirord1, symiirord2
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from .spline import *
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from .bsplines import *
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from .filter_design import *
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from .fir_filter_design import *
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from .ltisys import *
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from .lti_conversion import *
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from .signaltools import *
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from ._savitzky_golay import savgol_coeffs, savgol_filter
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from .spectral import *
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from .wavelets import *
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from ._peak_finding import *
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from .windows import get_window # keep this one in signal namespace
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# deal with * -> windows.* doc-only soft-deprecation
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deprecated_windows = ('boxcar', 'triang', 'parzen', 'bohman', 'blackman',
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'nuttall', 'blackmanharris', 'flattop', 'bartlett',
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'barthann', 'hamming', 'kaiser', 'gaussian',
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'general_gaussian', 'chebwin', 'cosine',
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'hann', 'exponential', 'tukey')
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# backward compatibility imports for actually deprecated windows not
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# in the above list
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from .windows import hanning
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def deco(name):
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f = getattr(windows, name)
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# Add deprecation to docstring
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def wrapped(*args, **kwargs):
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return f(*args, **kwargs)
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wrapped.__name__ = name
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wrapped.__module__ = 'scipy.signal'
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if hasattr(f, '__qualname__'):
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wrapped.__qualname__ = f.__qualname__
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if f.__doc__:
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lines = f.__doc__.splitlines()
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for li, line in enumerate(lines):
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if line.strip() == 'Parameters':
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break
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else:
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raise RuntimeError('dev error: badly formatted doc')
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spacing = ' ' * line.find('P')
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lines.insert(li, ('{0}.. warning:: scipy.signal.{1} is deprecated,\n'
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'{0} use scipy.signal.windows.{1} '
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'instead.\n'.format(spacing, name)))
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wrapped.__doc__ = '\n'.join(lines)
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return wrapped
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for name in deprecated_windows:
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locals()[name] = deco(name)
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del deprecated_windows, name, deco
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__all__ = [s for s in dir() if not s.startswith('_')]
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from scipy._lib._testutils import PytestTester
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test = PytestTester(__name__)
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del PytestTester
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