remez(numtaps, bands, desired, weight=None, Hz=None, type='bandpass', maxiter=25, grid_density=16, fs=None)
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.
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.
A monotonic sequence containing the band edges. All elements must be non-negative and less than half the sampling frequency as given by fs.
A sequence half the size of bands containing the desired gain in each of the specified bands.
The sampling frequency in Hz. Default is 1.
The type of filter:
Maximum number of iterations of the algorithm. Default is 25.
Grid density. The dense grid used in remez is of size (numtaps + 1) * grid_density. Default is 16.
The sampling frequency of the signal. Default is 1.
A rank-1 array containing the coefficients of the optimal (in a minimax sense) filter.
Calculate the minimax optimal filter using the Remez exchange algorithm.
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
fs = 22050 # Sample rate, Hz
def plot_response(w, h, title):
"Utility function to plot response functions"
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(w, 20*np.log10(np.abs(h)))
ax.set_ylim(-40, 5)
ax.grid(True)
ax.set_xlabel('Frequency (Hz)')
ax.set_ylabel('Gain (dB)')
ax.set_title(title)
cutoff = 8000.0 # Desired cutoff frequency, Hz
trans_width = 100 # Width of transition from pass to stop, Hz
numtaps = 325 # Size of the FIR filter.
taps = signal.remez(numtaps, [0, cutoff, cutoff + trans_width, 0.5*fs],
[1, 0], fs=fs)
w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
plot_response(w, h, "Low-pass Filter")
plt.show()
cutoff = 2000.0 # Desired cutoff frequency, Hz
trans_width = 250 # Width of transition from pass to stop, Hz
numtaps = 125 # Size of the FIR filter.
taps = signal.remez(numtaps, [0, cutoff - trans_width, cutoff, 0.5*fs],
[0, 1], fs=fs)
w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
plot_response(w, h, "High-pass Filter")
plt.show()
band = [2000, 5000] # Desired pass band, Hz
trans_width = 260 # Width of transition from pass to stop, Hz
numtaps = 63 # Size of the FIR filter.
edges = [0, band[0] - trans_width, band[0], band[1],
band[1] + trans_width, 0.5*fs]
taps = signal.remez(numtaps, edges, [0, 1, 0], fs=fs)
w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
plot_response(w, h, "Band-pass Filter")
plt.show()
band = [6000, 8000] # Desired stop band, Hz
trans_width = 200 # Width of transition from pass to stop, Hz
numtaps = 175 # Size of the FIR filter.
edges = [0, band[0] - trans_width, band[0], band[1],
band[1] + trans_width, 0.5*fs]
taps = signal.remez(numtaps, edges, [1, 0, 1], fs=fs)
w, h = signal.freqz(taps, [1], worN=2000, fs=fs)
plot_response(w, h, "Band-stop Filter")
plt.show()
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them