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使用 Scipy–Python

设计 IIR 带通切比雪夫 2 型滤波器

原文:https://www.geesforgeks.org/design-an-IIR-band-Chebyshev-type-2-filter-use-scipy-python/

IR 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，其特点是脉冲响应 h(t)/h(n)在某一点后不为零，而是无限延续。

什么是 IIR 切比雪夫滤波器？

IIR 切比雪夫滤波器是一种线性时不变滤波器，与巴特沃兹滤波器一样，但与巴特沃兹滤波器相比，它具有更陡的滚降。切比雪夫滤波器根据通带纹波和截止纹波等参数进一步分为切比雪夫ⅰ型和切比雪夫ⅱ型。

切比雪夫滤波器与巴特沃斯有何不同？

与巴特沃兹滤波器相比，切比雪夫滤波器具有更陡的滚降。

什么是切比雪夫 2 型滤波器？

切比雪夫类型 2 通过在阻带中加入相等的纹波，将整个阻带上理想和实际频率响应之间的绝对差异降至最低。

规格如下:

  • Pass band frequency: 1400-2100 Hz
  • Stop band frequency: 1050-24500 Hz
  • Pass band ripple: 0.4dB
  • Stop band attenuation: 50 dB
  • Sampling frequency: 7 kHz

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

第二步:定义用户自定义函数MFR eqz()T5】和T8】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)

    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()
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