alan@461: # Carfac.py - Cochlear filter model based on Dick Lyons work.  This material taken from his Hearing book (to be published)
alan@461: # Author: Al Strelzoff
alan@461: 
alan@461: from numpy import cos, sin, tan, sinh, arctan, pi, e, real,imag,arccos,arcsin,arctan2,log10,log
alan@461: 
alan@461: from pylab import figure, clf, plot,loglog, xlabel, ylabel, xlim, ylim, title, grid, axes, axis, show
alan@461: 
alan@461: fs = 22050.0            # sampling rate
alan@461: Nyq = fs/2.0            # nyquist frequency
alan@461: 
alan@461: 
alan@461: # given a frequency f, return the ERB
alan@461: def ERB_Hz(f):
alan@461: #    Ref: Glasberg and Moore: Hearing Research, 47 (1990), 103-138
alan@461:     return 24.7 * (1.0 + 4.37 * f / 1000.0)
alan@461: 
alan@461: 
alan@461: # ERB parameters
alan@461: ERB_Q = 1000.0/(24.7*4.37)  # 9.2645
alan@461: ERB_break_freq = 1000/4.37  # 228.833
alan@461: 
alan@461: ERB_per_step = 0.3333        
alan@461: 
alan@461: # set up channels
alan@461: 
alan@461: first_pole_theta = .78 * pi # We start at the top frequency.
alan@461: pole_Hz = first_pole_theta * fs / (2.0*pi)  # frequency of top pole
alan@461: min_pole_Hz = 40.0    # bottom frequency
alan@461: 
alan@461: # set up the pole frequencies according to the above parameters
alan@461: pole_freqs = []     # empty list of pole frequencies to fill, zeroth will be the top
alan@461: while pole_Hz >  min_pole_Hz:
alan@461:     pole_Hz = pole_Hz - ERB_per_step * ERB_Hz(pole_Hz)
alan@461:     pole_freqs.append(pole_Hz)
alan@461:     
alan@461: n_ch = len(pole_freqs)      # n_ch is the number of channels or frequency steps
alan@461: print('num channels',n_ch)
alan@461: 
alan@461: # Now we have n_ch, the number of channels, so can make the array of filters by instantiating the filter class (see below)
alan@461: 
alan@461: # before we make the filters, let's plot the position of the frequencies and the values of ERB at each.
alan@461: 
alan@461: fscale = []
alan@461: erbs = []
alan@461: 
alan@461: figure(0)
alan@461: for i in range(n_ch):
alan@461:     
alan@461:     f = pole_freqs[i]        # the frequencies from the list
alan@461:     ERB = ERB_Hz(f)       # the ERB value at each frequency
alan@461:     fscale.append(f)
alan@461:     erbs.append(ERB)
alan@461:     
alan@461: # plot a verticle hash at each frequency:
alan@461:     u = []
alan@461:     v = []
alan@461:     for j in range(5):
alan@461:         u.append(f)
alan@461:         v.append(10.0 + float(j))
alan@461: 
alan@461:     plot(u,v)  
alan@461:     
alan@461: loglog(fscale,erbs)
alan@461: 
alan@461: title('ERB scale')
alan@461: 
alan@461: 
alan@461: 
alan@461: # This filter class includes some methods useful only in design.  They will not be used in run time implementation.
alan@461: #  From figure 14.3 in Dick Lyon's book.
alan@461: 
alan@461: 
alan@461: #########################################################The Carfac filter class#################################################################################
alan@461: 
alan@461: # fixed parameters
alan@461: min_zeta = 0.12
alan@461: 
alan@461: class carfac():
alan@461:     
alan@461:     
alan@461:     # instantiate the class (in C++, the constructor)
alan@461:     def __init__(self,f):
alan@461:         
alan@461:         self.frequency = f
alan@461:        
alan@461:         theta = 2.0 * pi * f/fs
alan@461:        
alan@461:         r =  1.0 - sin(theta) * min_zeta
alan@461:         
alan@461:         
alan@461:         a = r * cos(theta)
alan@461:         c = r * sin(theta)
alan@461:         
alan@461:       
alan@461:         h = c
alan@461:         
alan@461:         g = 1.0/(1.0 + h * r * sin(theta) / (1.0 - 2.0 * r * cos(theta) + r ** 2))
alan@461:         
alan@461:         # make all parameters properties of the class 
alan@461:         self.a = a
alan@461:         self.c = c
alan@461:         self.r = r
alan@461:         self.theta = theta
alan@461:         self.h = h
alan@461:         self.g = g
alan@461:         
alan@461:         
alan@461:         # the two storage elements.  Referring to diagram 14.3 on p.263, z2 is the upper storage register, z1, the lower
alan@461:         self.z1 = 0.0    
alan@461:         self.z2 = 0.0    
alan@461:       
alan@461:         
alan@461:         # frequency response of this filter
alan@461:         self.H = []
alan@461:         
alan@461:        
alan@461:         
alan@461:         # the total  frequency magnitude of this filter including all the filters in front of this one
alan@461:         self.HT = []       # this list will be filled by multiplying all the H's ahead of it together with its own (H)
alan@461:         
alan@461:      
alan@461:        
alan@461:         
alan@461:          
alan@461:     
alan@461:     # execute one clock tick.  Take in one input and output one result. Execution semantics taken from fig. 14.3
alan@461:     #  This execution model is not tested in this file.  Here for reference.  See the file Exec.py for testing this execution model.  This is the main run time method.
alan@461:     def input(self,X):
alan@461: 
alan@461:         # recover the class definitions of these variables.  These statements below take up zero time at execution since they are just compiler declarations.
alan@461:         
alan@461:         
alan@461:         a = self.a
alan@461:         c = self.c
alan@461:         h = self.h
alan@461:         g = self.g
alan@461:         z1 = self.z1                    # z1 is the lower storage in fig. 14.3
alan@461:         z2 = self.z2
alan@461:         
alan@461:         # calculate what the next value of z1 will be, but don't overwrite current value yet.   
alan@461:         next_z1 = (a * z1) - (c * z2)   # Note: view this as next_z1 = a*z1 + (-c*z2) so that it is a 2 element multiply accumulate
alan@461:         # the output Y
alan@461:         Y = g * (X + h * next_z1)       # Note: reorganize this as Y = g*X + (g*h) * next_z1     g*h is a precomputed constant so then the form is a 2 element multiply accumulate.
alan@461:         
alan@461:         #stores
alan@461:         z2 = (a * z2) + (c * z1)        #Note: this is a 2 element multiply accumulate
alan@461:         z1 = next_z1
alan@461:         
alan@461:         return Y                        # The output
alan@461:     
alan@461:     # complex frequency response of this filter at frequency w.  That is, what it contributes to the cascade
alan@461:     # this method is used for test only.  It finds the frequency magnitude.  Not included in run time filter class.
alan@461:     def Hw(self,w):
alan@461: 
alan@461:         a = self.a
alan@461:         c = self.c
alan@461:         g = self.g
alan@461:         h = self.h
alan@461:         r = self.r
alan@461:         z = e ** (complex(0,w))         # w is in radians so this is z = exp(jw)
alan@461:         return g * (1.0 + (h*c*z)/(z**2 - 2.0*a*z + r**2 ))     # from page ?? of Lyon's book.   
alan@461:         
alan@461:         
alan@461:     # Note: to get the complex frequency response of this filter at frequency w, get Hw(w) and then compute arctan2(-imag(Hw(w))/-real(Hw(w)) + pi
alan@461:       
alan@461:     
alan@461:     
alan@461:     
alan@461:     
alan@461: ######################################################End of Carfac filter class########################################################################
alan@461:     
alan@461: # instantiate the filters
alan@461: 
alan@461: # n_ch is the number of filters as determined above
alan@461: 
alan@461: Filters = []    # the list of all filters, the zeroth is the top frequency
alan@461: for i in range(n_ch):
alan@461:     f = pole_freqs[i]
alan@461:     filter = carfac(f)  # note: get the correct parameters for r and h from Dick's matlab script.  Load them here from a table.
alan@461:     Filters.append(filter)
alan@461:     
alan@461: 
alan@461: 
alan@461: # sweep parameters
alan@461: steps = 1000
alan@461: 
alan@461: sum = []    # array to hold the magnitude sum
alan@461: for i in range(steps): sum.append( 0.0 )
alan@461: 
alan@461: figure(1)   
alan@461: title('CarFac  frequency response')
alan@461: 
alan@461: for i in range(n_ch):
alan@461:     filter = Filters[i]
alan@461:     # plotting arrays
alan@461:     u = []
alan@461:     v = []
alan@461:     # calculate the frequency magnitude by stepping the frequency in radians
alan@461:     for j in range(steps):
alan@461:         
alan@461:         w = pi * float(j)/steps
alan@461:         u.append(w)
alan@461:         mag = filter.Hw(w)      # freq mag at freq w
alan@461:         filter.H.append(mag)        # save for later use
alan@461:         filter.HT.append(mag)       # will be total response of cascade to this point after we do the multiplication in a step below
alan@461:         v.append(real(mag))           # y plotting axis
alan@461:         sum[j]+= mag    
alan@461:         
alan@461:       
alan@461:     plot(u,v)
alan@461:     
alan@461: 
alan@461: 
alan@461: figure(2)
alan@461: title('Summed frequency magnitudes')
alan@461: for i in range(steps): sum[i] = abs(sum[i])/n_ch
alan@461: plot(u,sum)
alan@461: 
alan@461: # calculate the phase response of the same group of  filters
alan@461: figure(3)
alan@461: title('Filter Phase')
alan@461: 
alan@461: 
alan@461: for i in range(n_ch):
alan@461:     filter = Filters[i]
alan@461:     
alan@461:     u = []
alan@461:     v = []
alan@461:     for j in range(steps):
alan@461:         x = float(j)/Nyq
alan@461:         
alan@461:         u.append(x)
alan@461:        
alan@461:         mag = filter.H[j]
alan@461:         phase = arctan2(-imag(mag),-real(mag)) + pi     # this formula used to avoid wrap around
alan@461:        
alan@461:         v.append(phase)           # y plotting axis 
alan@461:      
alan@461:     plot(u,v)
alan@461: 
alan@461:     
alan@461:     
alan@461: # calulate and plot cascaded frequency response and summed magnitude    
alan@461: sum = []    # array to hold the magnitude sum
alan@461: for i in range(steps): sum.append( 0.0 )
alan@461: 
alan@461: 
alan@461: figure(4)   
alan@461: title('CarFac Cascaded  frequency response')
alan@461: 
alan@461: 
alan@461: for i in range(n_ch-1):
alan@461:    
alan@461:     filter = Filters[i]
alan@461:     next = Filters[i+1]
alan@461:     
alan@461:     
alan@461:     u = []
alan@461:     v = []
alan@461:     for j in range(steps):
alan@461:         u.append(float(j)/Nyq)
alan@461:         mag = filter.HT[j] * next.HT[j]
alan@461:         filter.HT[j] = mag
alan@461:         v.append(real(mag))
alan@461:         sum[j]+= mag    
alan@461: 
alan@461:       
alan@461:     plot(u,v)
alan@461:    
alan@461:   
alan@461: 
alan@461: figure(5)
alan@461: title('Summed cascaded frequency magnitudes')
alan@461: for i in range(steps): sum[i] = abs(sum[i])/n_ch
alan@461: plot(u,sum)
alan@461: 
alan@461: # calculate and plot the phase responses of the cascaded filters
alan@461: 
alan@461: figure(6)
alan@461: title('Filter cascaded Phase')
alan@461: 
alan@461: 
alan@461: for i in range(n_ch):
alan@461:     filter = Filters[i]
alan@461:     
alan@461: 
alan@461:     u = []
alan@461:     v = []
alan@461:     for j in range(steps):
alan@461:         x = float(j)/Nyq
alan@461:         
alan@461:         u.append(x)
alan@461:         mag = filter.HT[j]
alan@461:         phase = arctan2(-imag(mag),-real(mag)) + pi
alan@461:           
alan@461:         v.append(phase)           # y plotting axis 
alan@461:         
alan@461:         
alan@461: 
alan@461:       
alan@461:     plot(u,v)
alan@461: 
alan@461: show()
alan@461: