如何用 Scipy–Python 实现 IIR 带通巴特沃斯滤波器？
原文:https://www.geesforgeks.org/如何实现-IIR-带通-巴特沃斯-滤波器-使用-scipy-python/
IIR 代表无限脉冲响应，它是许多线性时不变系统的显著特征之一，其特点是具有脉冲响应 h(t)/h(n) ，该脉冲响应在某一点后不变为零，而是无限延续。
什么是 IIR 带通巴特沃斯？
它基本上就像一个普通的数字带通巴特沃兹滤波器，具有无限的脉冲响应。
规格如下:
- 通带频率:1400-2100 赫兹
- 阻带频率:1050-24500 赫兹
- 通带纹波:0.4 分贝
- 阻带衰减:50 分贝
- 采样频率:7 千赫
我们将绘制滤波器的幅度、相位、脉冲和阶跃响应。
分步方法:
步骤 1: 导入所有必要的库。
蟒 3
# import required library
import numpy as np
import scipy.signal as signal
import matplotlib.pyplot as plt
步骤 2: 定义用户定义函数 mfreqz()和 impz() 。【mfreqz 是幅值和相位图的函数& impz 是脉冲和阶跃响应的函数】
python 3
def mfreqz(b, a, Fs):
# Compute frequency response of the filter
# using signal.freqz function
wz, hz = signal.freqz(b, a)
# Calculate Magnitude from hz in dB
Mag = 20*np.log10(abs(hz))
# Calculate phase angle in degree from hz
Phase = np.unwrap(np.arctan2(np.imag(hz), np.real(hz)))*(180/np.pi)
# Calculate frequency in Hz from wz
Freq = wz*Fs/(2*np.pi)
# Plot filter magnitude and phase responses using subplot.
fig = plt.figure(figsize=(10, 6))
# Plot Magnitude response
sub1 = plt.subplot(2, 1, 1)
sub1.plot(Freq, Mag, 'r', linewidth=2)
sub1.axis([1, Fs/2, -100, 5])
sub1.set_title('Magnitude Response', fontsize=20)
sub1.set_xlabel('Frequency [Hz]', fontsize=20)
sub1.set_ylabel('Magnitude [dB]', fontsize=20)
sub1.grid()
# Plot phase angle
sub2 = plt.subplot(2, 1, 2)
sub2.plot(Freq, Phase, 'g', linewidth=2)
sub2.set_ylabel('Phase (degree)', fontsize=20)
sub2.set_xlabel(r'Frequency (Hz)', fontsize=20)
sub2.set_title(r'Phase response', fontsize=20)
sub2.grid()
plt.subplots_adjust(hspace=0.5)
fig.tight_layout()
plt.show()
# Define impz(b,a) to calculate impulse response
# and step response of a system
# input: b= an array containing numerator coefficients,
# a= an array containing denominator coefficients
def impz(b, a):
# Define the impulse sequence of length 60
impulse = np.repeat(0., 60)
impulse[0] = 1.
x = np.arange(0, 60)
# Compute the impulse response
response = signal.lfilter(b, a, impulse)
# Plot filter impulse and step response:
fig = plt.figure(figsize=(10, 6))
plt.subplot(211)
plt.stem(x, response, 'm', use_line_collection=True)
plt.ylabel('Amplitude', fontsize=15)
plt.xlabel(r'n (samples)', fontsize=15)
plt.title(r'Impulse response', fontsize=15)
plt.subplot(212)
step = np.cumsum(response) # Compute step response of the system
plt.stem(x, step, 'g', use_line_collection=True)
plt.ylabel('Amplitude', fontsize=15)
plt.xlabel(r'n (samples)', fontsize=15)
plt.title(r'Step response', fontsize=15)
plt.subplots_adjust(hspace=0.5)
fig.tight_layout()
plt.show()
步骤 3: 用给定的过滤器规格定义变量。
蟒 3
# Given specification
Fs = 7000 # Sampling frequency in Hz
fp = np.array([1400, 2100]) # Pass band frequency in Hz
fs = np.array([1050, 2450]) # Stop band frequency in Hz
Ap = 0.4 # Pass band ripple in dB
As = 50 # stop band attenuation in dB
