Frequency Domain Modeling for Classification of Signals

A probability distribution model is proposed in this paper. Fourier Transform of a unit rectangular pulse, whose width is a random variable with Gaussian distribution, is used to derive the probability density function (p.d.f.) in the frequency domain. Result of the mathematical derivation is an exponential mathematical function involving an infinite summation over all integers. The projection theorem is used to arrive at the exact probability density function. To verify this experimentally, a randomly generated sample of Gaussian numbers, representing the pulse width is mapped onto the frequency domain, and the resulting points have a certain probability distribution, which matches with the theoretically proposed function.