I have a discrete sample of a function of time shaped like a decaying exponential that is not free of noise. My goal is to represent it in the frequency domain. I used the FFT but the results are very noisy.
Are there windows that allow this type of functions to be properly transformed (taking aside the noise coming from the meassuring process)? I know that I can fit the curve in the time domain to functional form whose Fourier transform is well known and then work in an analytical way. But I wish to known if the direct transform can be made successfully without such a fit and and what would be the advantages and disadvantages of doing so. Also, how would the above apply to the case where the sample is a mixture of an unknown number of exponential type functions.
Thanks in advance