FIR 滤波器¶
| 日期 | 2011-06-06（最后修改），2010-08-27（创建） |
|---|
此 Cookbook 示例展示了如何使用 scipy.signal 中的函数设计和使用低通 FIR 滤波器。
matplotlib 中的 pylab 模块用于创建绘图。
In [1]
#!python
from numpy import cos, sin, pi, absolute, arange
from scipy.signal import kaiserord, lfilter, firwin, freqz
from pylab import figure, clf, plot, xlabel, ylabel, xlim, ylim, title, grid, axes, show
#------------------------------------------------
# Create a signal for demonstration.
#------------------------------------------------
sample_rate = 100.0
nsamples = 400
t = arange(nsamples) / sample_rate
x = cos(2*pi*0.5*t) + 0.2*sin(2*pi*2.5*t+0.1) + \
0.2*sin(2*pi*15.3*t) + 0.1*sin(2*pi*16.7*t + 0.1) + \
0.1*sin(2*pi*23.45*t+.8)
#------------------------------------------------
# Create a FIR filter and apply it to x.
#------------------------------------------------
# The Nyquist rate of the signal.
nyq_rate = sample_rate / 2.0
# The desired width of the transition from pass to stop,
# relative to the Nyquist rate. We'll design the filter
# with a 5 Hz transition width.
width = 5.0/nyq_rate
# The desired attenuation in the stop band, in dB.
ripple_db = 60.0
# Compute the order and Kaiser parameter for the FIR filter.
N, beta = kaiserord(ripple_db, width)
# The cutoff frequency of the filter.
cutoff_hz = 10.0
# Use firwin with a Kaiser window to create a lowpass FIR filter.
taps = firwin(N, cutoff_hz/nyq_rate, window=('kaiser', beta))
# Use lfilter to filter x with the FIR filter.
filtered_x = lfilter(taps, 1.0, x)
#------------------------------------------------
# Plot the FIR filter coefficients.
#------------------------------------------------
figure(1)
plot(taps, 'bo-', linewidth=2)
title('Filter Coefficients (%d taps)' % N)
grid(True)
#------------------------------------------------
# Plot the magnitude response of the filter.
#------------------------------------------------
figure(2)
clf()
w, h = freqz(taps, worN=8000)
plot((w/pi)*nyq_rate, absolute(h), linewidth=2)
xlabel('Frequency (Hz)')
ylabel('Gain')
title('Frequency Response')
ylim(-0.05, 1.05)
grid(True)
# Upper inset plot.
ax1 = axes([0.42, 0.6, .45, .25])
plot((w/pi)*nyq_rate, absolute(h), linewidth=2)
xlim(0,8.0)
ylim(0.9985, 1.001)
grid(True)
# Lower inset plot
ax2 = axes([0.42, 0.25, .45, .25])
plot((w/pi)*nyq_rate, absolute(h), linewidth=2)
xlim(12.0, 20.0)
ylim(0.0, 0.0025)
grid(True)
#------------------------------------------------
# Plot the original and filtered signals.
#------------------------------------------------
# The phase delay of the filtered signal.
delay = 0.5 * (N-1) / sample_rate
figure(3)
# Plot the original signal.
plot(t, x)
# Plot the filtered signal, shifted to compensate for the phase delay.
plot(t-delay, filtered_x, 'r-')
# Plot just the "good" part of the filtered signal. The first N-1
# samples are "corrupted" by the initial conditions.
plot(t[N-1:]-delay, filtered_x[N-1:], 'g', linewidth=4)
xlabel('t')
grid(True)
show()
最终的绘图显示了原始信号（细蓝色线）、滤波后的信号（通过适当的相位延迟移位以与原始信号对齐；细红色线）以及滤波后的信号的“良好”部分（粗绿色线）。“良好部分”是信号中不受初始条件影响的部分。
章节作者：WarrenWeckesser
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