One of the most significant problems in many application areas is to extract the required signal from background noise. Background noise is random, the occurrence of signal and the behaviour of signal are also random. Therefore, it is practical to deal with the signal extraction problem using methods based on probability theory and statistical estimation. That is to say that signal detection and parameter estimation problems are statistical hypothesis testing problems in mathematical statistics. In this paper, signal and noise environment is encountered in active sonar system for target detection. The optimum receiver is presented for range-Doppler-shift processing in a background-noise-limited environment using linear frequency modulation pulse .FFT based implementation for target detection of active sonar system using MATLAB has been shown here.