Module SciPy.signal.filter

Variables

EPSILON

EPSILON = 2e-16

abs

abs = absolute

band_dict

band_dict = { Const('band') : Const('bandpass'), Const('bandpass') : Const('bandpass'), Const('pass') : Const('bandpass'), Const('bp') : Const('bandpass'), Const('bs') : Const('bandstop'), Const('bandstop') : Const('bandstop'), Const('bands') : Const('bandstop'), Const('stop') : Const('bandstop'), Const('l') : Const('lowpass'), Const('low') : Const('lowpass'), Const('lowpass') : Const('lowpass'), Const('high') : Const('highpass'), Const('highpass') : Const('highpass'), Const('h') : Const('highpass') }

filter_dict

filter_dict = { Const('butter') : List([Name('buttap'), Name('buttord')]), Const('butterworth') : List([Name('buttap'), Name('buttord')]), Const('cauer') : List([Name('ellipap'), Name('ellipord')]), Const('elliptic') : List([Name('ellipap'), Name('ellipord')]), Const('ellip') : List([Name('ellipap'), Name('ellipord')]), Const('bessel') : List([Name('besselap')]), Const('cheby1') : List([Name('cheb1ap'), Name('cheb1ord')]), Const('chebyshev1') : List([Name('cheb1ap'), Name('cheb1ord')]), Const('chebyshevi') : List([Name('cheb1ap'), Name('cheb1ord')]), Const('cheby2') : List([Name('cheb2ap'), Name('cheb2ord')]), Const('chebyshev2') : List([Name('cheb2ap'), Name('cheb2ord')]), Const('chebyshevii') : List([Name('cheb2ap'), Name('cheb2ord')]) }

Function summary

band_stop_obj(wp, ind, passb, stopb, gpass, gstop, type)

bessel(N, Wn, btype = 'low', analog = 0, output = 'ba')

besselap(N)

bilinear(b, a, fs = 1.0)

buttap(N)

butter(N, Wn, btype = 'low', analog = 0, output = 'ba')

buttord(wp, ws, gpass, gstop, analog = 0)

cheb1ap(N, rp)

cheb1ord(wp, ws, gpass, gstop, analog = 0)

cheb2ap(N, rs)

cheb2ord(wp, ws, gpass, gstop, analog = 0)

cheby1(N, rp, Wn, btype = 'low', analog = 0, output = 'ba')

cheby2(N, rs, Wn, btype = 'low', analog = 0, output = 'ba')

ellip(N, rp, rs, Wn, btype = 'low', analog = 0, output = 'ba')

ellipap(N, rp, rs)

ellipord(wp, ws, gpass, gstop, analog = 0)

findfreqs(num, den, N)

firwin(N, cutoff, width = None, window = 'hamming')

freqs(b, a, worN = None, plot = None)

freqz(b, a = 1, worN = None, whole = 0, plot = None)

iirdesign(wp, ws, gpass, gstop, analog = 0, ftype = 'ellip', output = 'ba')

iirfilter(N, Wn, rp = None, rs = None, btype = 'band', analog = 0, ftype = 'butter', output = 'ba')

kaiserord(ripple, width)

kratio(m, k_ratio)

lp2bp(b, a, wo = 1.0, bw = 1.0)

lp2bs(b, a, wo = 1, bw = 1)

lp2hp(b, a, wo = 1.0)

lp2lp(b, a, wo = 1.0)

maxflat()

normalize(b, a)

tf2zpk(b, a)

vratio(u, ineps, mp)

yulewalk()

zpk2tf(z, p, k)

Functions

band_stop_obj(wp, ind, passb, stopb, gpass, gstop, type)

Band Stop Objective Function for order minimization

Description:

Returns the non-integer order for an analog band stop filter.

Inputs:

wp -- passb edge ind -- index specifying which passb edge to vary (0 or 1). passb -- two element vector of fixed passband edges. stopb -- two element vector of fixed stopband edges. gstop -- amount in dB of attenuation in stopband. gpass -- amount in dB of ripple in the passband. type -- 'butter', 'cheby', or 'ellip':

Outputs: (n,)

n -- filter order (possibly non-integer)

bessel(N, Wn, btype = 'low', analog = 0, output = 'ba')

Bessel digital and analog filter design.

Description:

Design an Nth order lowpass digital or analog Bessel filter and return the filter coefficients in (B,A) or (Z,P,K) form.

besselap(N)

Return (z,p,k) zero, pole, gain for analog prototype of an Nth order Bessel filter.

bilinear(b, a, fs = 1.0)

Return a digital filter from an analog filter using the bilinear transform.

The bilinear transform substitutes (z-1) / (z+1) for s

buttap(N)

Return (z,p,k) zero, pole, gain for analog prototype of an Nth order Butterworth filter.

butter(N, Wn, btype = 'low', analog = 0, output = 'ba')

Butterworth digital and analog filter design.

Description:

Design an Nth order lowpass digital or analog Butterworth filter and return the filter coefficients in (B,A) or (Z,P,K) form.

See also buttord.

buttord(wp, ws, gpass, gstop, analog = 0)

Butterworth filter order selection.

Description:

  Return the order of the lowest order digital Butterworth filter that
  loses no more than gpass dB in the passband and has at least gstop dB
  attenuation in the stopband.

Inputs:

  wp, ws -- Passband and stopband edge frequencies, normalized from 0
            to 1 (1 corresponds to pi radians / sample).  For example:
               Lowpass:   wp = 0.2,          ws = 0.3
               Highpass:  wp = 0.3,          ws = 0.2
               Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
               Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
  gpass -- The maximum loss in the passband (dB).
  gstop -- The minimum attenuation in the stopband (dB).
  analog -- Non-zero to design an analog filter (in this case wp and
            ws are in radians / second).

Outputs: (ord, Wn)

  ord -- The lowest order for a Butterworth filter which meets specs.
  Wn -- The Butterworth natural frequency (i.e. the "3dB frequency").
        Should be used with scipy.signal.butter to give filter results.

cheb1ap(N, rp)

Return (z,p,k) zero, pole, gain for Nth order Chebyshev type I lowpass analog filter prototype with rp decibels of ripple in the passband.

cheb1ord(wp, ws, gpass, gstop, analog = 0)

Chebyshev type I filter order selection.

Description:

  Return the order of the lowest order digital Chebyshev Type I filter
  that loses no more than gpass dB in the passband and has at least gstop dB
  attenuation in the stopband.

Inputs:

  wp, ws -- Passband and stopband edge frequencies, normalized from 0
            to 1 (1 corresponds to pi radians / sample).  For example:
               Lowpass:   wp = 0.2,          ws = 0.3
               Highpass:  wp = 0.3,          ws = 0.2
               Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
               Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
  gpass -- The maximum loss in the passband (dB).
  gstop -- The minimum attenuation in the stopband (dB).
  analog -- Non-zero to design an analog filter (in this case wp and
            ws are in radians / second).

Outputs: (ord, Wn)

  ord -- The lowest order for a Chebyshev type I filter that meets specs.
  Wn -- The Chebyshev natural frequency (the "3dB frequency") for
        use with scipy.signal.cheby1 to give filter results.

cheb2ap(N, rs)

Return (z,p,k) zero, pole, gain for Nth order Chebyshev type II lowpass analog filter prototype with rs decibels of ripple in the stopband.

cheb2ord(wp, ws, gpass, gstop, analog = 0)

Chebyshev type II filter order selection.

Description:

  Return the order of the lowest order digital Chebyshev Type II filter
  that loses no more than gpass dB in the passband and has at least gstop dB
  attenuation in the stopband.

Inputs:

  wp, ws -- Passband and stopband edge frequencies, normalized from 0
            to 1 (1 corresponds to pi radians / sample).  For example:
               Lowpass:   wp = 0.2,          ws = 0.3
               Highpass:  wp = 0.3,          ws = 0.2
               Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
               Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
  gpass -- The maximum loss in the passband (dB).
  gstop -- The minimum attenuation in the stopband (dB).
  analog -- Non-zero to design an analog filter (in this case wp and
            ws are in radians / second).

Outputs: (ord, Wn)

  ord -- The lowest order for a Chebyshev type II filter that meets specs.
  Wn -- The Chebyshev natural frequency for
        use with scipy.signal.cheby2 to give the filter.

cheby1(N, rp, Wn, btype = 'low', analog = 0, output = 'ba')

Chebyshev type I digital and analog filter design.

Description:

Design an Nth order lowpass digital or analog Chebyshev type I filter and return the filter coefficients in (B,A) or (Z,P,K) form.

See also ellipord.

ellipap(N, rp, rs)

Return (z,p,k) zeros, poles, and gain of an Nth order normalized prototype elliptic analog lowpass filter with rp decibels of ripple in the passband and a stopband rs decibels down.

See Chapter 12 and Chapter 5 of "Filter Design for Signal Processing", by Lutova, Tosic, and Evans. This is

ellipord(wp, ws, gpass, gstop, analog = 0)

Elliptic (Cauer) filter order selection.

Description:

  Return the order of the lowest order digital elliptic filter
  that loses no more than gpass dB in the passband and has at least
  gstop dB attenuation in the stopband.

Inputs:

  wp, ws -- Passband and stopband edge frequencies, normalized from 0
            to 1 (1 corresponds to pi radians / sample).  For example:
               Lowpass:   wp = 0.2,          ws = 0.3
               Highpass:  wp = 0.3,          ws = 0.2
               Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
               Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
  gpass -- The maximum loss in the passband (dB).
  gstop -- The minimum attenuation in the stopband (dB).
  analog -- Non-zero to design an analog filter (in this case wp and
            ws are in radians / second).

Outputs: (ord, Wn)

  ord -- The lowest order for an Elliptic (Cauer) filter that meets specs.
  Wn  -- The natural frequency for use with scipy.signal.ellip
           to give the filter.

findfreqs(num, den, N)

firwin(N, cutoff, width = None, window = 'hamming')

FIR Filter Design using windowed ideal filter method.

Inputs:

  N      -- order of filter (number of taps)
  cutoff -- cutoff frequency of filter (normalized so that 1 corresponds to
              Nyquist or pi radians / sample)

  width  -- if width is not None, then assume it is the approximate width of
              the transition region (normalized so that 1 corresonds to pi)
              for use in kaiser FIR filter design.
  window -- desired window to use.

Outputs:

  h      -- coefficients of length N fir filter.

freqs(b, a, worN = None, plot = None)

Compute frequency response of analog filter.

Description:

   Given the numerator (b) and denominator (a) of a filter compute its
   frequency response.

           b[0]*(jw)**(nb-1) + b[1]*(jw)**(nb-2) + ... + b[nb-1]
   H(w) = --------------------------------------------------------
           a[0]*(jw)**(na-1) + a[1]*(jw)**(na-2) + ... + a[na-1]

Inputs:

   b, a --- the numerator and denominator of a linear filter.
   worN --- If None, then compute at 200 frequencies around the interesting
            parts of the response curve (determined by pole-zero locations).
            If a single integer, the compute at that many frequencies.
            Otherwise, compute the response at frequencies given in worN.
Outputs: (w,h)

   w -- The frequencies at which h was computed.
   h -- The frequency response.

freqz(b, a = 1, worN = None, whole = 0, plot = None)

Compute frequency response of a digital filter.

Description:

   Given the numerator (b) and denominator (a) of a digital filter compute
   its frequency response.

              jw               -jw            -jmw
       jw  B(e)    b[0] + b[1]e + .... + b[m]e
    H(e) = ---- = ------------------------------------
              jw               -jw            -jnw
           A(e)    a[0] + a[2]e + .... + a[n]e

Inputs:

   b, a --- the numerator and denominator of a linear filter.
   worN --- If None, then compute at 512 frequencies around the unit circle.
            If a single integer, the compute at that many frequencies.
            Otherwise, compute the response at frequencies given in worN
   whole -- Normally, frequencies are computed from 0 to pi (upper-half of
            unit-circle.  If whole is non-zero compute frequencies from 0
            to 2*pi.

Outputs: (w,h)

   w -- The frequencies at which h was computed.
   h -- The frequency response.

iirdesign(wp, ws, gpass, gstop, analog = 0, ftype = 'ellip', output = 'ba')

Complete IIR digital and analog filter design.

Description:

  Given passband and stopband frequencies and gains construct an analog or
  digital IIR filter of minimum order for a given basic type.  Return the
  output in numerator, denominator ('ba') or pole-zero ('zpk') form.

Inputs:

  wp, ws -- Passband and stopband edge frequencies, normalized from 0
            to 1 (1 corresponds to pi radians / sample).  For example:
               Lowpass:   wp = 0.2,          ws = 0.3
               Highpass:  wp = 0.3,          ws = 0.2
               Bandpass:  wp = [0.2, 0.5],   ws = [0.1, 0.6]
               Bandstop:  wp = [0.1, 0.6],   ws = [0.2, 0.5]
  gpass -- The maximum loss in the passband (dB).
  gstop -- The minimum attenuation in the stopband (dB).
  analog -- Non-zero to design an analog filter (in this case wp and
            ws are in radians / second).
  ftype -- The type of iir filter to design:
             elliptic    : 'ellip'
             Butterworth : 'butter',
             Chebyshev I : 'cheby1',
             Chebyshev II: 'cheby2',
             Bessel :      'bessel'
  output -- Type of output:  numerator/denominator ('ba') or pole-zero ('zpk')

Outputs: (b,a) or (z,p,k)

  b,a -- Numerator and denominator of the iir filter.
  z,p,k -- Zeros, poles, and gain of the iir filter.

iirfilter(N, Wn, rp = None, rs = None, btype = 'band', analog = 0, ftype = 'butter', output = 'ba')

IIR digital and analog filter design given order and critical points.

Description:

  Design an Nth order lowpass digital or analog filter and return the filter
  coefficients in (B,A) (numerator, denominator) or (Z,P,K) form.

Inputs:

  N -- the order of the filter.
  Wn -- a scalar or length-2 sequence giving the critical frequencies.
  rp, rs -- For chebyshev and elliptic filters provides the maximum ripple
            in the passband and the minimum attenuation in the stop band.
  btype -- the type of filter (lowpass, highpass, bandpass, or bandstop).
  analog -- non-zero to return an analog filter, otherwise
            a digital filter is returned.
  ftype -- the type of IIR filter (Butterworth, Cauer (Elliptic),
           Bessel, Chebyshev1, Chebyshev2)
  output -- 'ba' for (b,a) output, 'zpk' for (z,p,k) output.

SEE ALSO butterord, cheb1ord, cheb2ord, ellipord

kaiserord(ripple, width)

Design a Kaiser window to limit ripple and width of transition region.

Inputs:

ripple -- positive number specifying maximum ripple in passband (dB)

and minimum ripple in stopband

width -- width of transition region (normalized so that 1 corresponds

to pi radians / sample)

Outputs:

N, beta -- the order and beta parameter for the kaiser window.

signal.kaiser(N,beta,sym=0) returns the window as does signal.get_window(beta,N) signal.get_window(('kaiser',beta),N)

Uses the empirical equations discovered by Kaiser.

Oppenheim, Schafer, "Discrete-Time Signal Processing,", p.475-476.

kratio(m, k_ratio)

lp2bp(b, a, wo = 1.0, bw = 1.0)

Return a band-pass filter with center frequency wo and bandwidth bw from a low-pass filter prototype with unity cutoff frequency.

lp2bs(b, a, wo = 1, bw = 1)

Return a band-stop filter with center frequency wo and bandwidth bw from a low-pass filter prototype with unity cutoff frequency.

lp2hp(b, a, wo = 1.0)

Return a high-pass filter with cuttoff frequency wo from a low-pass filter prototype with unity cutoff frequency.

lp2lp(b, a, wo = 1.0)

Return a low-pass filter with cuttoff frequency wo from a low-pass filter prototype with unity cutoff frequency.

maxflat()

normalize(b, a)

Normalize polynomial representation of a transfer function.

tf2zpk(b, a)

Return zero, pole, gain (z,p,k) representation from a numerator, denominator representation of a linear filter.

vratio(u, ineps, mp)

yulewalk()

zpk2tf(z, p, k)

Return polynomial transfer function representation from zeros and poles

Inputs:

z, p --- sequences representing the zeros and poles. k --- system gain.

Outputs: (b,a)

b, a --- numerator and denominator polynomials.

Imported Names

Local name	Refers to
absolute	numpy.absolute
allclose	numpy.allclose
arccosh	numpy.arccosh
arcsinh	numpy.arcsinh
arctan	numpy.arctan
asarray	numpy.asarray
atleast_1d	numpy.atleast_1d
ceil	numpy.ceil
comb	scipy.misc.comb
conjugate	numpy.conjugate
cos	numpy.cos
cosh	numpy.cosh
exp	numpy.exp
log10	numpy.log10
logspace	numpy.logspace
mintypecode	numpy.mintypecode
numpy	numpy
optimize	scipy.optimize
pi	numpy.pi
poly	numpy.poly
polyval	numpy.polyval
real	numpy.real
resize	numpy.resize
roots	numpy.roots
r_	numpy.r_
sinh	numpy.sinh
special	scipy.special
sqrt	numpy.sqrt
string	string
tan	numpy.tan
types	types
zeros	numpy.zeros

Local name

Refers to

absolute

numpy.absolute

allclose

numpy.allclose

arccosh

numpy.arccosh

arcsinh

numpy.arcsinh

arctan

numpy.arctan

asarray

numpy.asarray

atleast_1d

numpy.atleast_1d

ceil

numpy.ceil

comb

scipy.misc.comb

conjugate

numpy.conjugate

cos

numpy.cos

cosh

numpy.cosh

exp

numpy.exp

log10

numpy.log10

logspace

numpy.logspace

mintypecode

numpy.mintypecode

numpy

optimize

scipy.optimize

numpy.pi

poly

numpy.poly

polyval

numpy.polyval

real

numpy.real

resize

numpy.resize

roots

numpy.roots

numpy.r_

sinh

numpy.sinh

special

scipy.special

sqrt

numpy.sqrt

string

tan

numpy.tan

types

zeros

numpy.zeros

Module SciPy.​signal.​filter_design

Variables

Function summary

Functions

Imported Names

Module SciPy.signal.filter_design