The aim of this paper is to present the details of signal processing techniques in radars. These techniques are strongly based on mathematics and especially on stochastic processes. Detecting a target in a noisy environment is a many folds sequential process. Two applications of the suggested sonar detector will be discussed: the cross-correlator detector and the matched filter detector. In each scenario, we are interested in the detector's output while the input signal is free of noise and when the signal is contaminated by noise, which is considered to be Gaussian noise. Due to the reduced complexity and computation time associated with the matched filter construction, the cross-correlator detector's complexity can be solved.
Additionally, this article presents a digital implementation of a modified recursive tapped delay line integrator (transversal filter). A delay line constructed using analogue techniques has a big dimension and is unstable. Many of these issues are addressed by the digital application of this filter. Additionally, this work offers a digital implementation of a modified recursive SPMF (Single Pulse Matched Filter) and a modified recursive matched filter. Thus, an optimal sonar detector is developed and implemented using a digitally updated recursive matching filter.