# Stimulus / rate reconstruction with Wiener Kernels.

by Beserra
Tags: kernels, neuron, rate, reconstruction, stimulus, wiener
 P: 2 Hello. 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 FD = G./FQSS' 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! Beserra
 P: 2 I forgot to specify that Qab denotes the cross correlation function of a and b

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