Evaluation of a Class of Quadratic Gauss Sums by Sampling a Continuous Chirp Signal

The calculation of Discrete Fourier Transform (DFT) of a periodic discrete-time chirp ends in the evaluation of a quadratic Gauss sum. The calculation of this sum has not been an easy problem in mathematics. It has taken years to be solved. In this work, by sampling a continuous chirp and relating the spectrum of the signal and the spectrum of its samples, an interesting solution to the calculation of a class of Gauss sums is presented. The solution once again reveals the beauties of signal processing techniques.