Python 基于基于FIR实现实现Hilbert滤波器求信号包络详解滤波器求信号包络详解
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在通信领域,可以通过希尔伯特变换求解解析信号,进而求解窄带信号的包络。
实现希尔伯特变换有两种方法,一种是对信号做FFT,单后只保留单边频谱,在做IFFT,我们称之为频域方法;另一种是基于
FIR根据传递函数设计一个希尔伯特滤波器,我们称之为时域方法。
# -*- coding:utf8 -*-
# @TIME : 2019/4/11 18:30
# @Author : SuHao
# @File : hilberfilter.py
import scipy.signal as signal
import numpy as np
import librosa as lib
import matplotlib.pyplot as plt
import time
# from preprocess_filter import *
# 读取音频文件
ex = '..\..\数据集2\pre2012\bflute\BassFlute.ff.C5B5.aiff'
time_series, fs = lib.load(ex, sr=None, mono=True, res_type='kaiser_best')
# 生成一个chirp信号
# duration = 2.0
# fs = 400.0
# samples = int(fs*duration)
# t = np.arange(samples) / fs
# time_series = signal.chirp(t, 20.0, t[-1], 100.0)
# time_series *= (1.0 + 0.5 * np.sin(2.0*np.pi*3.0*t) )
def hilbert_filter(x, fs, order=201, pic=None):
'''
:param x: 输入信号
:param fs: 信号采样频率
:param order: 希尔伯特滤波器阶数
:param pic: 是否绘图,bool
:return: 包络信号
'''
co = [2*np.sin(np.pi*n/2)**2/np.pi/n for n in range(1, order+1)]
co1 = [2*np.sin(np.pi*n/2)**2/np.pi/n for n in range(-order, 0)]
co = co1+[0]+ co
# out = signal.filtfilt(b=co, a=1, x=x, padlen=int((order-1)/2))
out = signal.convolve(x, co, mode='same', method='direct')
envolope = np.sqrt(out**2 + x**2)
if pic is not None:
w, h = signal.freqz(b=co, a=1, worN=2048, whole=False, plot=None, fs=2*np.pi)
fig, ax1 = plt.subplots()
ax1.set_title('hilbert filter frequency response')
ax1.plot(w, 20 * np.log10(abs(h)), 'b')
ax1.set_ylabel('Amplitude [dB]', color='b')
ax1.set_xlabel('Frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(h))
ax2.plot(w, angles, 'g')
ax2.set_ylabel('Angle (radians)', color='g')
ax2.grid()
ax2.axis('tight')
# plt.savefig(pic + 'hilbert_filter.jpg')
plt.show()
# plt.clf()
# plt.close()
return envolope
start = time.time()
env0 = hilbert_filter(time_series, fs, 81, pic=True)
end = time.time()
a = end-start
print(a)
plt.figure()
ax1 = plt.subplot(211)
plt.plot(time_series)
ax2 = plt.subplot(212)
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