Stimulus / rate reconstruction with Wiener Kernels.

by Beserra
Tags: kernels, neuron, rate, reconstruction, stimulus, wiener
Beserra is offline
Jan17-14, 07:30 AM
P: 2

I am having some trouble trying to reconstruct my firing rates using a Volterra expansion.
Basically it is known that , if :
s(t) = the value of a given stimulus at time t
r(t) = the firing rate of a neuron at time t

then we assume that a possible estimate of the firing rate can be achieved by
rest(t) = r_0 + ∫dτ D(τ)s(t-τ) where D(τ) is the Wiener Kernel.

Then the condition for the best estimate rest(t) is achieved when
FD(ω)*FQss(ω) = FQrs(-ω) . Where FA denotes the fourier transform of a function A.

While I understand all this mathematically I can not apply it using Matlab.
I have s as a vector of positions of a given stimulus and rg as a vector of
rates of a neuron .

Then I make
QSS = xcorr(S,S);
QrS = xcorr(rg,S);
FQSS = fft(QSS);
FQrS = fft(QrS);
G = FQrS(length(FQrS):-1:1); % G(ω) = FQrS(-ω) because xcorr seems to put the t = 0
%at the middle of the vector
D = ifft(FD);

When I make 'rest' proportional to 'conv(D, S)' I obtain not my firing rates but rather
a very similar version of my own stimulus S.

What am I doing wrong? Thanks!

Phys.Org News Partner Biology news on
Humpback protections downgrade clears way for pipeline
Researchers discover the most effective animal signal strategies
Maine baby lobster decline could end high catches
Beserra is offline
Jan17-14, 07:32 AM
P: 2
I forgot to specify that Qab denotes the cross correlation function of a and b

Register to reply

Related Discussions
Tax Cuts vs Government Stimulus Current Events 19
A stimulus leading to hiccup Biology 5
Stimulus firing Calculus & Beyond Homework 0
Results of the Stimulus Plan General Discussion 24
Stimulus: buy unproductive assets Current Events 9