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threetube.py
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threetube.py
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#coding:utf-8
#
# Three Tube Model, A python Class to calculate frequecny response and procee reflection transmission of resonance tube
#
import numpy as np
from matplotlib import pyplot as plt
# Check version
# Python 3.6.4 on win32 (Windows 10)
# numpy 1.14.0
class Class_ThreeTube(object):
def __init__(self, L3, A3, L1=9.0, L2=8.0, A1=1.0, A2=7.0, rg0=0.95, rl0=0.9 ,sampling_rate=48000):
# initalize Tube length and Tube area
self.L1= L1 # set list of 1st tube's length by unit is [cm]
self.A1= A1 # set list of 1st tube's area by unit is [cm^2]
self.L2= L2 # set list of 2nd tube's length by unit is [cm]
self.A2= A2 # set list of 2nd tube's area by unit is [cm^2]
self.L3= L3 # set list of 3rd tube's length by unit is [cm]
self.A3= A3 # set list of 3rd tube's area by unit is [cm^2]
C0=35000.0 # speed of sound in air, round 35000 cm/second
self.sr= sampling_rate
self.tu1=self.L1 / C0 # delay time in 1st tube
self.tu2=self.L2 / C0 # delay time in 2nd tube
self.tu3=self.L3 / C0 # delay time in 3rd tube
self.r1=( self.A2 - self.A1) / ( self.A2 + self.A1) # reflection coefficient between 1st tube and 2nd tube
self.r2=( self.A3 - self.A2) / ( self.A3 + self.A2) # reflection coefficient between 2nd tube and 3rd tube
self.rg0=rg0 # rg is reflection coefficient between glottis and 1st tube
self.rl0=rl0 # reflection coefficient between 3rd tube and mouth
def fone(self, xw):
# calculate one point of frequecny response
yi= 0.5 * ( 1.0 + self.rg0 ) * ( 1.0 + self.r1) * ( 1.0 + self.r2) * ( 1.0 + self.rl0 ) * np.exp( -1.0j * ( self.tu1 + self.tu2 + self.tu3 ) * xw)
yb1= 1.0 + self.r1 * self.rg0 * np.exp( -2.0j * self.tu1 * xw )
yb1= yb1 + self.r2 * self.r1 * np.exp( -2.0j * self.tu2 * xw )
yb1= yb1 + self.rl0 * self.r2 * np.exp( -2.0j * self.tu3 * xw )
yb2= self.r2 * self.rg0 * np.exp( -2.0j * (self.tu1 + self.tu2) * xw )
yb2= yb2 + self.rl0 * self.r1 * np.exp( -2.0j * (self.tu2 + self.tu3) * xw )
yb3= self.rl0 * self.r2 * self.r1 * self.rg0 * np.exp( -2.0j * (self.tu1 + self.tu3) * xw )
yb4= self.rl0 * self.rg0 * np.exp( -2.0j * (self.tu1 + self.tu2 + self.tu3) * xw )
yb= yb1 + yb2 + yb3 + yb4
val= yi/yb
return np.sqrt(val.real ** 2 + val.imag ** 2)
def H0(self, freq_low=100, freq_high=5000, 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 * 2.0 * np.pi))
return np.log10(amp) * 20, bands # = amp value, freq list
def process(self, yg ):
# process reflection transmission of resonance tube: yg is input, y2tm is output
# three serial resonance tube
# ---------------------
# | |
# ------------------- --------
# | |
# | |
# ------------------- |--------
# | |
# ---------------------
# reflection ratio
# rg r1 r2 rl0
# ya1---(forward)---> yb1---(forward)---> yc1 ---(foward) --->
# <-----(backward)--ya2 <---(backward)---yb2 <---(backward)--yc2
# input yg output y2tm
#
#
M1= round( self.tu1 * self.sr ) + 1 # for precision, higher sampling_rate is better
M2= round( self.tu2 * self.sr ) + 1 # for precision, higher sampling_rate is better
M3= round( self.tu3 * self.sr ) + 1 # for precision, higher sampling_rate is better
M1= int(M1)
M2= int(M2)
M3= int(M3)
ya1=np.zeros(M1)
ya2=np.zeros(M1)
yb1=np.zeros(M2)
yb2=np.zeros(M2)
yc1=np.zeros(M3)
yc2=np.zeros(M3)
y2tm=np.zeros(len(yg))
for tc0 in range(len(yg)):
for i in range((M1-1),0,-1): # process one step
ya1[i]=ya1[i-1]
ya2[i]=ya2[i-1]
for i in range((M2-1),0,-1): # process one step
yb1[i]=yb1[i-1]
yb2[i]=yb2[i-1]
for i in range((M3-1),0,-1): # process one step
yc1[i]=yc1[i-1]
yc2[i]=yc2[i-1]
# calculate reflection
ya1[0]= ((1. + self.rg0 ) / 2.) * yg[tc0] + self.rg0 * ya2[-1]
ya2[0]= -1. * self.r1 * ya1[-1] + ( 1. - self.r1 ) * yb2[-1]
yb1[0]= ( 1 + self.r1 ) * ya1[-1] + self.r1 * yb2[-1]
yb2[0]= -1. * self.r2 * yb1[-1] + ( 1. - self.r2 ) * yc2[-1]
yc1[0]= ( 1 + self.r2 ) * yb1[-1] + self.r2 * yc2[-1]
yc2[0]= -1. * self.rl0 * yc1[-1]
y2tm[tc0]= (1 + self.rl0) * yc1[-1]
return y2tm
if __name__ == '__main__':
# Length & Area value, from problems 3.8 in "Digital Processing of Speech Signals" by L.R.Rabiner and R.W.Schafer
#
# /a/
L1_a=9.0 # set list of 1st tube's length by unit is [cm]
A1_a=1.0 # set list of 1st tube's area by unit is [cm^2]
L2_a=8.0 # set list of 2nd tube's length by unit is [cm]
A2_a=7.0 # set list of 2nd tube's area by unit is [cm^2]
# /u/
L1_u=10.0 # set list of 1st tube's length by unit is [cm]
A1_u=7.0 # set list of 1st tube's area by unit is [cm^2]
L2_u=7.0 # set list of 2nd tube's length by unit is [cm]
A2_u=3.0 # set list of 2nd tube's area by unit is [cm^2]
# /o/: L3,A3 is extend factor to /a/ connecting as /u/
L3_o= L2_a * (L2_u / L1_u) # set list of 3rd tube's length by unit is [cm]
A3_o= A2_a * (A2_u / A1_u) # set list of 3rd tube's area by unit is [cm^2]
# insatnce
threetube_o = Class_ThreeTube(L3_o,A3_o)
#This file uses TAB