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BPF4.py
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BPF4.py
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#coding:utf-8
#
# A class of IIR Band Pass Filter, process twice !
# (Target response is 2nd harmonic level less than -70dB)
#
import sys
import numpy as np
from matplotlib import pyplot as plt
from scipy import signal
from iir1 import *
from ema1 import *
# Check version
# Python 3.6.4 on win32 (Windows 10)
# numpy 1.14.0
# matplotlib 2.1.1
# scipy 1.4.1
class Class_BPFtwice(object):
def __init__(self, fc=1000, gain=1.0, Q=40.0, sampling_rate=48000, moving_average_factor=None, down_sample_factor=None ):
# initalize
self.sr= sampling_rate
self.fc= fc # center frequency of Band Pass Filter by unit is [Hz]
self.gain= gain # magnification
self.Q= Q # Q factor
# check Q
if self.Q <= 0.0:
print ('error: Q must be > 0. filter becomes flat. (Class_BPF)')
# sys.exit()
self.a= np.array( [ 1.0, 0.0, 0.0])
self.b= np.array( [ 1.0, 0.0, 0.0])
else:
self.a, self.b = self.bpf1()
#-------------------------------------
# set for filtering2
#
# Exponential Moving Average with Half-wave rectification, and smoothing via lpf
if moving_average_factor is not None:
self.maf= moving_average_factor
self.ema= Class_EMA1(N=self.maf)
else:
self.ema= None
# Down sampling to decrease temporal resolution
if down_sample_factor is None:
self.down_sample_factor= 1
else:
self.down_sample_factor= int(down_sample_factor)
#
#--------------------------------------
def bpf1(self,):
# primary digital filter
a= np.zeros(3)
b= np.zeros(3)
wc= 2.0 * np.pi * self.fc / self.sr
g0= 2.0 * np.tan( wc/2.0)
a[0]= 4.0 + 2.0 * g0 / self.Q + g0 * g0
a[1]= -8.0 + 2.0 * g0 * g0
a[2]= 4.0 - 2.0 * g0 / self.Q + g0 * g0
b[0]= 2.0 * self.gain * g0 / self.Q
b[2]= -2.0 * self.gain * g0 / self.Q
b /= a[0]
a /= a[0]
return a,b
def iir2(self,x):
# calculate iir filter: x is input, y is output
# y[0]= b[0] * x[0] + b[1] * x[-1] + b[2] * x[-1]
# y[0]= y[0] - a[1] * y[-1] - a[2] * y[-1]
y= np.zeros(len(x))
for n in range(len(x)):
for i in range(len(self.b)):
if n - i >= 0:
y[n] += self.b[i] * x[n - i]
for j in range(1, len(self.a)):
if n - j >= 0:
y[n] -= self.a[j] * y[n - j]
return y
def fone(self, xw):
# calculate one point of frequecny response
f= xw / self.sr
yi= self.b[0] + self.b[1] * np.exp(-2j * np.pi * f) + self.b[2] * np.exp(-2j * np.pi * 2 * f)
yb= self.a[0] + self.a[1] * np.exp(-2j * np.pi * f) + self.a[2] * np.exp(-2j * np.pi * 2 * f)
val= yi/yb
val= val * val
return np.sqrt(val.real ** 2 + val.imag ** 2)
def H0(self, freq_low=100, freq_high=7500, Band_num=256):
# get Log scale frequecny response, from freq_low to freq_high, Band_num points
amp=[]
freq=[]
bands= np.zeros(Band_num+1)
fcl=freq_low * 1.0 # convert to float
fch=freq_high * 1.0 # convert to float
delta1=np.power(fch/fcl, 1.0 / (Band_num)) # Log Scale
bands[0]=fcl
#print ("i,band = 0", bands[0])
for i in range(1, Band_num+1):
bands[i]= bands[i-1] * delta1
#print ("i,band =", i, bands[i])
for f in bands:
amp.append(self.fone(f))
return np.log10(amp) * 20, bands # = amp value, freq list
def H0_show(self,freq_low=100, freq_high=7500, Band_num=256):
# draw frequecny response
plt.xlabel('Hz')
plt.ylabel('dB')
plt.title('Band Pass Filter')
amp, freq=self.H0(freq_low=freq_low, freq_high=freq_high, Band_num=Band_num)
plt.plot(freq, amp)
plt.grid()
plt.show()
def filtering(self, xin):
# filtering process, using scipy
return signal.lfilter(self.b, self.a, self.filtering0(xin))
def filtering0(self, xin):
# filtering process, using scipy
return signal.lfilter(self.b, self.a, xin)
def filtering2(self, xin, dwn_len):
# xin should be mono
# (1)filtering process, using scipy
# (2)Exponential Moving Average with Half-wave rectification, and smoothing via lpf
# (3)down sampling
self.dwn_len=dwn_len
return np.resize( self.ema ( self.filtering(xin) ) , (self.dwn_len, self.down_sample_factor))[:,0]
def check_minphase(self,):
zeros, poles, _ = signal.tf2zpk(self.b, self.a)
print ( zeros)
print ( poles)
for kai in np.concatenate([zeros,poles]):
if not np.abs(kai) < 1.0:
print ('This is not min phase')
def f_show(self, worN=1024):
# show frequency response, using scipy
wlist, fres = signal.freqz(self.b, self.a, worN=worN)
fres= fres * fres
fig = plt.figure()
ax1 = fig.add_subplot(111)
flist = wlist / ((2.0 * np.pi) / self.sr)
plt.title('frequency response')
ax1 = fig.add_subplot(111)
plt.semilogx(flist, 20 * np.log10(abs(fres)), 'b') # plt.plot(flist, 20 * np.log10(abs(fres)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [Hz]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(fres))
angles = angles / ((2.0 * np.pi) / 360.0)
plt.semilogx(flist, angles, 'g') # plt.plot(flist, angles, 'g')
plt.ylabel('Angle(deg)', color='g')
plt.grid()
plt.axis('tight')
plt.show()
def wav_show(self,y1,y2=None, y3=None):
# draw wavform
plt.figure()
plt.subplot(311)
plt.xlabel('time step')
plt.ylabel('amplitude')
tlist= np.arange( len(y1) ) * (1 /self.sr)
plt.plot( tlist, y1)
if y2 is not None:
plt.subplot(312)
plt.xlabel('time step')
plt.ylabel('amplitude')
tlist= np.arange( len(y2) ) * (1 /self.sr)
plt.plot( tlist, y2)
if y3 is not None:
plt.subplot(313)
plt.xlabel('time step')
plt.ylabel('amplitude')
tlist= np.arange( len(y3) ) * (1 /self.sr)
plt.plot( tlist, y3)
plt.grid()
plt.axis('tight')
plt.show()
if __name__ == '__main__':
from scipy import signal
from scipy.io.wavfile import read as wavread
# instance
fc1=1000
dsf=10
Q0=40.0
bpf=Class_BPFtwice(fc=fc1, Q=Q0, sampling_rate=44100, moving_average_factor=80, down_sample_factor=dsf)
# draw frequecny response
bpf.H0_show(freq_high=20000)
# draw frequecny response, using scipy
bpf.f_show()
# load a sample wav
#path0='wav/400Hz-10dB_44100Hz_400msec.wav'
#path0='wav/1KHz-10dB_44100Hz_400msec.wav'
#path0='wav/3KHz-10dB_44100Hz_400msec.wav'
#path0='wav/5KHz-10dB_44100Hz_400msec.wav'
path0='wav/1KHz-10dB_44100Hz_400ms-TwoTube_stereo.wav'
try:
sr, y = wavread(path0)
except:
print ('error: wavread ')
sys.exit()
else:
yg= y / (2 ** 15)
if yg.ndim == 2: # if stereo
yg= np.average(yg, axis=1)
print ('sampling rate ', sr)
print ('y.shape', yg.shape)
y2=bpf.filtering( yg) # iir2( yg)
# Exponential Moving Average with Half-wave rectification
ema1= Class_EMA1()
y3=ema1( y2)
bpf.wav_show(yg, y2, y3)
# compare both for check
y5=bpf.filtering2(yg, int(len(yg)/dsf))
print ('y5.shape', y5.shape)
bpf.wav_show(yg,y3,y5)