Can anyone please give an example of an unequally spaced signal? If possible please suggest me any paper regarding the understanding of USFFT and its algorithm.
Have a look at http://amath.colorado.edu/faculty/beylkin/papers/applusfft.pdf
I haven't used the USFFT myself, but I can give you an example of what you call an unequally-spaced signal. You've probably seen an electrocardiogram (ECG), which is a recording of the electrical activity of the heart. The ECG looks like a series of pulses, and in normal conditions, all of these pulses have a well-known shape, which can be divided in five segments called P, Q, R, S, and T, where R denotes the highest point of the peak. It is often useful to compute the heart-rate variability (HRV), which is a function that assigns to each R peak the time elapsed between that peak and the previous one. In other words, it is the inverse of the heart rate (the heart period, we could say). Since the heart rate is dynamic, the R peaks are not equally spaced, and therefore, the HRV can be seen as an unequally-spaced signal.
.. I might be wrong Alfonso, but I think "unequally spaced" refers to the samples, not the features in the signal... The traditional FFT algorithm is designed for equally spaced points so here it is just requested if a computationally efficient one is available for unevenly spaced data. IMHO the answer depends on the spacing of the data. If it is just slightly uneven you can simply smear your signal (e.g. by a gaussian kernel) and use the FFT on a narrowly resampled data. I did not know the link proposed by Herbert Homeier so thanks for sharing.
In my archive I had this http://www.lanl.gov/DLDSTP/fast/
I think you can find further information online if you look for NUFFT, or the NFFT and PFFT libraries
Take a look at the Lomb periodogram and at the book "Numerical Recipes in C". As for an example, a very good example is the series of RR intervals as mentioned by Alfonso Alba above.
See e.g. http://www.tu-chemnitz.de/~potts/nfft/ for various applications and software.
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