.. currentmodule:: brian

.. index::
   pair: example usage; cos
   pair: example usage; log
   pair: example usage; ControlFilterbank
   pair: example usage; FunctionFilterbank
   pair: example usage; sinh
   pair: example usage; whitenoise
   pair: example usage; LinearFilterbank
   pair: example usage; sin
   pair: example usage; arcsinh

.. _example-hears_time_varying_filter2:

Example: time_varying_filter2 (hears)
=====================================

This example implements a band pass filter whose center frequency is modulated by
a sinusoid function. This modulator is implemented as a
:class:`~brian.hears.FunctionFilterbank`. One  state variable (here time) must
be kept; it is therefore implemented with a class.
The bandpass filter coefficients update is an example of how to use a
:class:`~brian.hears.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 = 1 # the filter coefficients are updated every sample
    
    mean_center_freq = 4*kHz #mean frequency around which the CF will oscillate
    amplitude = 1500*Hz      #amplitude of the oscillation
    frequency = 10*Hz        #frequency of the oscillation
    
    #this class is used in a FunctionFilterbank (via its __call__). It outputs the
    #center frequency of the band pass filter. Its output is thus later passed as
    #input to the controler. 
    class CenterFrequencyGenerator(object):
        def __init__(self): 
            self.t=0*second
       
        def __call__(self, input):
            #update of the center frequency
            fc = mean_center_freq+amplitude*sin(2*pi*frequency*self.t)
            #update of the state variable
            self.t = self.t+1./samplerate 
            return fc
    
    center_frequency = CenterFrequencyGenerator()      
    
    fc_generator = FunctionFilterbank(sound, center_frequency)
    
    #the updater of the controller generates new filter coefficient of the band pass
    #filter based on the center frequency it receives from the fc_generator
    #(its input)
    class CoeffController(object):
        def __init__(self, target):
            self.BW = 2*arcsinh(1./2/Q)*1.44269
            self.target=target
            
        def __call__(self, input):
            fc = input[-1,:] #the control variables are taken as the last of the buffer
            w0 = 2*pi*fc/array(samplerate)    
            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, fc_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=samplerate, noverlap=240)
    imshow(flipud(pxx), aspect='auto')
    
    show()