Stimulus / rate reconstruction with Wiener Kernels.

  1. 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!

  2. jcsd
  3. I forgot to specify that Qab denotes the cross correlation function of a and b
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