Fitting a convolution

Hi

I have the following piece of code:

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dataX = -4:1:4;
dataY = [0 -1 -10 -40 -55 10 40 10 1];

figure(1)
plot(dataX, dataY, '*');

x = -2:0.01:2;
plot(-4:0.01:4, 1*conv(exp(-x).*heaviside(x),sin(x)), dataX, dataY, '*')

mdl = @(a, x)(a(1)*conv(exp(-x).*heaviside(x),sin(x)));

par=[1];
[fitted_par, r, J, cov, mse] = nlinfit(dataX, dataY, mdl, par);

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What I am trying to do is to fit the function (a convolution) to the data set. However, I get an error due to vector size mismatch. I'm not sure what is going on here: The fitting routine should not care about how many data points I have?

Regards, Niels.

Answer 1

[Andrei Bobrov]

Try

mdl = @(a, x)a*conv(exp(-x).*heaviside(x),sin(x),'same');
[fitted_par, r, J, cov, mse] = nlinfit(dataX, dataY, mdl, 1);

[Niles Martinsen]

Hi

Thanks for replying. It runs now, but the fit gives me the amplitude 48.17, which is a horrible guess. Is something wrong with the program, or is it just a difficult function to fit?

Best regards,

Niels.

Answer 2

[Niles Martinsen]

Andrei's suggestion works, but when I increase the resolution of x, then the convolution changes as well. Is this just a property on conv, or have I made an error?