def remez(numtaps,
bands,
desired,
weight=None,
Hz=1,
type='bandpass',
maxiter=25,
grid_density=16):
"""Calculate the minimax optimal filter using Remez exchange algorithm.
Description:
Calculate the filter-coefficients for the finite impulse response
(FIR) filter whose transfer function minimizes the maximum error
between the desired gain and the realized gain in the specified bands
using the remez exchange algorithm.
Inputs:
numtaps -- The desired number of taps in the filter.
bands -- A montonic sequence containing the band edges. All elements
must be non-negative and less than 1/2 the sampling frequency
as given by Hz.
desired -- A sequency half the size of bands containing the desired gain
in each of the specified bands
weight -- A relative weighting to give to each band region.
type --- The type of filter:
'bandpass' : flat response in bands.
'differentiator' : frequency proportional response in bands.
Outputs: (out,)
out -- A rank-1 array containing the coefficients of the optimal
(in a minimax sense) filter.
"""
# Convert type
try:
tnum = {'bandpass': 1, 'differentiator': 2}[type]
except KeyError:
raise ValueError, "Type must be 'bandpass', or 'differentiator'"
# Convert weight
if weight is None:
weight = [1] * len(desired)
bands = asarray(bands).copy()
return sigtools._remez(numtaps, bands, desired, weight, tnum, Hz, maxiter,
grid_density)
def remez(numtaps, bands, desired, weight=None, Hz=1, type='bandpass',
maxiter=25, grid_density=16):
"""Calculate the minimax optimal filter using Remez exchange algorithm.
Description:
Calculate the filter-coefficients for the finite impulse response
(FIR) filter whose transfer function minimizes the maximum error
between the desired gain and the realized gain in the specified bands
using the remez exchange algorithm.
Inputs:
numtaps -- The desired number of taps in the filter.
bands -- A montonic sequence containing the band edges. All elements
must be non-negative and less than 1/2 the sampling frequency
as given by Hz.
desired -- A sequency half the size of bands containing the desired gain
in each of the specified bands
weight -- A relative weighting to give to each band region.
type --- The type of filter:
'bandpass' : flat response in bands.
'differentiator' : frequency proportional response in bands.
Outputs: (out,)
out -- A rank-1 array containing the coefficients of the optimal
(in a minimax sense) filter.
"""
# Convert type
try:
tnum = {'bandpass':1, 'differentiator':2}[type]
except KeyError:
raise ValueError, "Type must be 'bandpass', or 'differentiator'"
# Convert weight
if weight is None:
weight = [1] * len(desired)
bands = asarray(bands).copy()
return sigtools._remez(numtaps, bands, desired, weight, tnum, Hz,
maxiter, grid_density)
def remez(numtaps, bands, desired, weight=None, Hz=1, type='bandpass',
maxiter=25, grid_density=16):
"""
Calculate the minimax optimal filter using the Remez exchange algorithm.
Calculate the filter-coefficients for the finite impulse response
(FIR) filter whose transfer function minimizes the maximum error
between the desired gain and the realized gain in the specified
frequency bands using the Remez exchange algorithm.
Parameters
----------
numtaps : int
The desired number of taps in the filter. The number of taps is
the number of terms in the filter, or the filter order plus one.
bands : array_like
A monotonic sequence containing the band edges in Hz.
All elements must be non-negative and less than half the sampling
frequency as given by `Hz`.
desired : array_like
A sequence half the size of bands containing the desired gain
in each of the specified bands.
weight : array_like, optional
A relative weighting to give to each band region. The length of
`weight` has to be half the length of `bands`.
Hz : scalar, optional
The sampling frequency in Hz. Default is 1.
type : {'bandpass', 'differentiator', 'hilbert'}, optional
The type of filter:
'bandpass' : flat response in bands. This is the default.
'differentiator' : frequency proportional response in bands.
'hilbert' : filter with odd symmetry, that is, type III
(for even order) or type IV (for odd order)
linear phase filters.
maxiter : int, optional
Maximum number of iterations of the algorithm. Default is 25.
grid_density : int, optional
Grid density. The dense grid used in `remez` is of size
``(numtaps + 1) * grid_density``. Default is 16.
Returns
-------
out : ndarray
A rank-1 array containing the coefficients of the optimal
(in a minimax sense) filter.
See Also
--------
freqz : Compute the frequency response of a digital filter.
References
----------
.. [1] J. H. McClellan and T. W. Parks, "A unified approach to the
design of optimum FIR linear phase digital filters",
IEEE Trans. Circuit Theory, vol. CT-20, pp. 697-701, 1973.
.. [2] J. H. McClellan, T. W. Parks and L. R. Rabiner, "A Computer
Program for Designing Optimum FIR Linear Phase Digital
Filters", IEEE Trans. Audio Electroacoust., vol. AU-21,
pp. 506-525, 1973.
Examples
--------
We want to construct a filter with a passband at 0.2-0.4 Hz, and
stop bands at 0-0.1 Hz and 0.45-0.5 Hz. Note that this means that the
behavior in the frequency ranges between those bands is unspecified and
may overshoot.
>>> bpass = sp.signal.remez(72, [0, 0.1, 0.2, 0.4, 0.45, 0.5], [0, 1, 0])
>>> freq, response = sp.signal.freqz(bpass)
>>> ampl = np.abs(response)
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(111)
>>> ax1.semilogy(freq/(2*np.pi), ampl, 'b-') # freq in Hz
[<matplotlib.lines.Line2D object at 0xf486790>]
>>> plt.show()
"""
# Convert type
try:
tnum = {'bandpass':1, 'differentiator':2, 'hilbert':3}[type]
except KeyError:
raise ValueError("Type must be 'bandpass', 'differentiator', or 'hilbert'")
# Convert weight
if weight is None:
weight = [1] * len(desired)
bands = np.asarray(bands).copy()
return sigtools._remez(numtaps, bands, desired, weight, tnum, Hz,
maxiter, grid_density)