I made several guesses as to what you are doing, but this seems to work:
% Create data:
t = linspace(0, 1, 40);
C = t;
% y = conv(t,exp(-t),'same');
y = conv(exp(-t/7),t);
% Objective function for curve fit
% w = @(P,t) conv(C, exp(-t/P),'same');
w = @(P,t) conv(C, exp(-t/P));
xv = 0:length(y)-1;
B = nlinfit(t, y, w, 1)
yp = w(B,t);
figure(1)
plot(xv, y, 'xb')
hold on
plot(xv, w(B,t), '-r')
hold off
grid
Note that there are 'full', 'same' and 'valid' options with the conv function. Use the one that most closely suits your needs.
