The "problem" that the function is not defined at negative times tau is a common one: it also happens e.g. in cross- and auto-correlation formulae. A real-world sampled signal always is measured during a finite period of time (mostly starting by convention at t=0), but mathematically the formulae assume an integration from -infinity to +infinity. You may look at the real signal as a product of an ideal one (unlimited in time) and a rectangular window function with value 1 between time=0 and time=T and 0 elsewhere. A Fourier transform of a (bounded in time) function can therefore be considered as the convolution of the Fourier transform of the (unbounded in time) function with the Fourier transform of a rectangular function (which is an x/sin(x) f
untion, AFAI recall). In order to minimize the related artefacts in FFT, people often use other than rectangular window functions before FFT'ing, the 'Hanning' and the 'Hamming' type functions being most widely used.
I don't know if for the formula you are evaluating also such a windowing 'trick' is possible to reduce the artifacts of the function being defined only between 0 and T, but to start with, I would simply assume that fcc(tau) is 0 for tau<0 and for tau>T.
(PS: another argument why in your formula a functional relation and not a product is meant: if it were a product, the integrand could be converted like
[fcc*(taumax+tau)-fcc*(taumax-tau)]^2=fcc^2*[2*tau]^2=4*fcc^2*tau^2, i.e. taumax wouldn't appear any more...)
regards
Franz
