Difference equations play a vital role in the analysis of discrete changing sequences. In this paper, Stochastic Delay Interval Difference Equation (SDIDE) and its application on Amplitude Modulation (AM) are analyzed. In this analysis, a low-frequency information signal with randomly varying amplitude at different time intervals is depicted as a delay interval of a Langevin equation. The information signal can be retrieved by estimating the variance of the received signal. The following SDIDE is taken for analysis. y(n)=y(n-T)+T F(y(n),y(n-T))+EG(y(n))B(n) where F(y(n),y(n-T)) and G(y(n)) are known equations. The delay interval is T, E is a parameter which scales the noise amplitude and B(n) is a Brownian process. From the analysis, it is proved that the variance of the output is linearly proportional to the square of the delay interval of the input.

Stochastic delay interval difference equation; Amplitude modulation; Amplitude demodulation; Square law device; Low pass filter.