# Example: time_varying_filter1 (hears)ΒΆ

This example implements a band pass filter whose center frequency is modulated
by an Ornstein-Uhlenbeck. The white noise term used for this process is output
by a FunctionFilterbank. The bandpass filter coefficients update is an example
of how to use a `ControlFilterbank`

. The bandpass filter is
a basic biquadratic filter for which the Q factor and the center frequency must
be given. The input is a white noise.

```
from brian import *
from brian.hears import *
samplerate = 20*kHz
SoundDuration = 300*ms
sound = whitenoise(SoundDuration, samplerate).ramp()
#number of frequency channel (here it must be one as a spectrogram of the
#output is plotted)
nchannels = 1
fc_init = 5000*Hz #initial center frequency of the band pass filter
Q = 5 #quality factor of the band pass filter
update_interval = 4 # the filter coefficients are updated every 4 samples
#parameters of the Ornstein-Uhlenbeck process
s_i = 1200*Hz
tau_i = 100*ms
mu_i = fc_init/tau_i
sigma_i = sqrt(2)*s_i/sqrt(tau_i)
deltaT = defaultclock.dt
#this function is used in a FunctionFilterbank. It outputs a noise term that
#will be later used by the controler to update the center frequency
noise = lambda x: mu_i*deltaT+sigma_i*randn(1)*sqrt(deltaT)
noise_generator = FunctionFilterbank(sound, noise)
#this class will take as input the output of the noise generator and as target
#the bandpass filter center frequency
class CoeffController(object):
def __init__(self, target):
self.target = target
self.deltaT = 1./samplerate
self.BW = 2*arcsinh(1./2/Q)*1.44269
self.fc = fc_init
def __call__(self, input):
#the control variables are taken as the last of the buffer
noise_term = input[-1,:]
#update the center frequency by updateing the OU process
self.fc = self.fc-self.fc/tau_i*self.deltaT+noise_term
w0 = 2*pi*self.fc/samplerate
#update the coefficient of the biquadratic filterbank
alpha = sin(w0)*sinh(log(2)/2*self.BW*w0/sin(w0))
self.target.filt_b[:, 0, 0] = sin(w0)/2
self.target.filt_b[:, 1, 0] = 0
self.target.filt_b[:, 2, 0] = -sin(w0)/2
self.target.filt_a[:, 0, 0] = 1+alpha
self.target.filt_a[:, 1, 0] = -2*cos(w0)
self.target.filt_a[:, 2, 0] = 1-alpha
# In the present example the time varying filter is a LinearFilterbank therefore
#we must initialise the filter coefficients; the one used for the first buffer computation
w0 = 2*pi*fc_init/samplerate
BW = 2*arcsinh(1./2/Q)*1.44269
alpha = sin(w0)*sinh(log(2)/2*BW*w0/sin(w0))
filt_b = zeros((nchannels, 3, 1))
filt_a = zeros((nchannels, 3, 1))
filt_b[:, 0, 0] = sin(w0)/2
filt_b[:, 1, 0] = 0
filt_b[:, 2, 0] = -sin(w0)/2
filt_a[:, 0, 0] = 1+alpha
filt_a[:, 1, 0] = -2*cos(w0)
filt_a[:, 2, 0] = 1-alpha
#the filter which will have time varying coefficients
bandpass_filter = LinearFilterbank(sound, filt_b, filt_a)
#the updater
updater = CoeffController(bandpass_filter)
#the controller. Remember it must be the last of the chain
control = ControlFilterbank(bandpass_filter, noise_generator, bandpass_filter,
updater, update_interval)
time_varying_filter_mon = control.process()
figure(1)
pxx, freqs, bins, im = specgram(squeeze(time_varying_filter_mon),
NFFT=256, Fs=float(samplerate), noverlap=240)
imshow(flipud(pxx), aspect='auto')
show()
```