firls(numtaps, bands, desired, weight=None, nyq=None, fs=None)
Calculate the filter coefficients for the linear-phase finite impulse response (FIR) filter which has the best approximation to the desired frequency response described by bands
and :None:None:`desired` in the least squares sense (i.e., the integral of the weighted mean-squared error within the specified bands is minimized).
This implementation follows the algorithm given in . As noted there, least squares design has multiple advantages:
Optimal in a least-squares sense.
Simple, non-iterative method.
The general solution can obtained by solving a linear system of equations.
Allows the use of a frequency dependent weighting function.
This function constructs a Type I linear phase FIR filter, which contains an odd number of :None:None:`coeffs` satisfying for $n < numtaps$
:
The odd number of coefficients and filter symmetry avoid boundary conditions that could otherwise occur at the Nyquist and 0 frequencies (e.g., for Type II, III, or IV variants).
The number of taps in the FIR filter. :None:None:`numtaps` must be odd.
A monotonic nondecreasing sequence containing the band edges in Hz. All elements must be non-negative and less than or equal to the Nyquist frequency given by :None:None:`nyq`.
A sequence the same size as bands
containing the desired gain at the start and end point of each band.
A relative weighting to give to each band region when solving the least squares problem. :None:None:`weight` has to be half the size of bands
.
Deprecated. Use `fs` instead. Nyquist frequency. Each frequency in bands
must be between 0 and :None:None:`nyq` (inclusive). Default is 1.
The sampling frequency of the signal. Each frequency in bands
must be between 0 and fs/2
(inclusive). Default is 2.
Coefficients of the optimal (in a least squares sense) FIR filter.
FIR filter design using least-squares error minimization.
We want to construct a band-pass filter. Note that the behavior in the frequency ranges between our stop bands and pass bands is unspecified, and thus may overshoot depending on the parameters of our filter:
>>> from scipy import signal
... import matplotlib.pyplot as plt
... fig, axs = plt.subplots(2)
... fs = 10.0 # Hz
... desired = (0, 0, 1, 1, 0, 0)
... for bi, bands in enumerate(((0, 1, 2, 3, 4, 5), (0, 1, 2, 4, 4.5, 5))):
... fir_firls = signal.firls(73, bands, desired, fs=fs)
... fir_remez = signal.remez(73, bands, desired[::2], fs=fs)
... fir_firwin2 = signal.firwin2(73, bands, desired, fs=fs)
... hs = list()
... ax = axs[bi]
... for fir in (fir_firls, fir_remez, fir_firwin2):
... freq, response = signal.freqz(fir)
... hs.append(ax.semilogy(0.5*fs*freq/np.pi, np.abs(response))[0])
... for band, gains in zip(zip(bands[::2], bands[1::2]),
... zip(desired[::2], desired[1::2])):
... ax.semilogy(band, np.maximum(gains, 1e-7), 'k--', linewidth=2)
... if bi == 0:
... ax.legend(hs, ('firls', 'remez', 'firwin2'),
... loc='lower center', frameon=False)
... else:
... ax.set_xlabel('Frequency (Hz)')
... ax.grid(True)
... ax.set(title='Band-pass %d-%d Hz' % bands[2:4], ylabel='Magnitude') ...
>>> fig.tight_layout()
... plt.show()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._fir_filter_design.firwin
scipy.signal._fir_filter_design.firwin2
scipy.signal._fir_filter_design.firls
scipy.signal._fir_filter_design.remez
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