# -*- coding:utf-8 -*- # Author:凌逆战 | Never # Date: 2023/1/1 """ 绘制 窗函数和对应的频率响应 """ import numpy as np from numpy.fft import rfft import matplotlib.pyplot as plt window_len = 60 # frequency response def frequency_response(window, window_len=window_len, NFFT=2048): A = rfft(window, NFFT) / (window_len / 2) # (513,) mag = np.abs(A) freq = np.linspace(0, 0.5, len(A)) # 忽略警告 with np.errstate(divide='ignore', invalid='ignore'): response = 20 * np.log10(mag) response = np.clip(response, -150, 150) return freq, response def Rectangle_windows(win_length): # 矩形窗 return np.ones((win_length)) def Voibis_windows(win_length): """ Voibis_windows窗函数，RNNoise使用的是它，它满足Princen-Bradley准则。 :param x: :param win_length: 窗长 :return: """ x = np.arange(0, win_length) return np.sin((np.pi / 2) * np.sin((np.pi * x) / win_length) ** 2) def sqrt_hanning_windows(win_length, mode="periodic"): # symmetric: 对称窗，主要用于滤波器的设计 # periodic: 周期窗，常用于频谱分析 if mode == "symmetric": haning_window = np.hanning(win_length) sqrt_haning_window = np.sqrt(haning_window) elif mode == "periodic": haning_window = np.hanning(win_length+1) sqrt_haning_window = np.sqrt(haning_window) sqrt_haning_window = sqrt_haning_window[0:-1].astype('float32') return sqrt_haning_window Rectangle_windows = Rectangle_windows(window_len) hanning_window = np.hanning(M=window_len) print(np.argmax(hanning_window)) sqrt_hanning_windows = sqrt_hanning_windows(window_len) hamming_window = np.hamming(M=window_len) Voibis_windows = Voibis_windows(window_len) blackman_window = np.blackman(M=window_len) bartlett_window = np.bartlett(M=window_len) kaiser_window = np.kaiser(M=window_len, beta=14) plt.figure() plt.plot(Rectangle_windows, label="Rectangle") plt.plot(hanning_window, label="hanning") plt.plot(sqrt_hanning_windows, label="sqrt_hanning") plt.plot(hamming_window, label="hamming") plt.plot(Voibis_windows, label="Voibis") plt.plot(blackman_window, label="blackman") plt.plot(bartlett_window, label="bartlett") plt.plot(kaiser_window, label="kaiser") plt.legend() plt.tight_layout() plt.show() freq, Rectangle_FreqResp = frequency_response(Rectangle_windows, window_len) freq, hanning_FreqResp = frequency_response(hanning_window, window_len) freq, sqrt_hanning_FreqResp = frequency_response(sqrt_hanning_windows, window_len) freq, hamming_FreqResp = frequency_response(hamming_window, window_len) freq, Voibis_FreqResp = frequency_response(Voibis_windows, window_len) freq, blackman_FreqResp = frequency_response(blackman_window, window_len) freq, bartlett_FreqResp = frequency_response(bartlett_window, window_len) freq, kaiser_FreqRespw = frequency_response(kaiser_window, window_len) plt.figure() plt.title("Frequency response") plt.plot(freq, Rectangle_FreqResp, label="Rectangle") plt.plot(freq, hanning_FreqResp, label="hanning") plt.plot(freq, sqrt_hanning_FreqResp, label="sqrt_hanning") plt.plot(freq, hamming_FreqResp, label="hamming") plt.plot(freq, Voibis_FreqResp, label="Voibis") plt.plot(freq, blackman_FreqResp, label="blackman") plt.plot(freq, bartlett_FreqResp, label="bartlett") plt.plot(freq, kaiser_FreqRespw, label="kaiser") plt.ylabel("Magnitude [dB]") plt.xlabel("Normalized frequency [cycles per sample]") plt.legend() plt.tight_layout() plt.show()