Pulse Compression is one of the key steps in the signal processing of a Radar system. Radar system uses Pulse compression techniques to provide the benefits of larger range detection and high range resolution. This is gained by modulating the transmitted signal and after that matching the received echo with the transmitted signal. Matched filter is used as the pulse compression filter which provides high SNR at the output. Matched Filter is a time reversed and conjugated version of the received radar signal. There are several methods of pulse compression that have been used in the past, out of which most popular technique is Linear Frequency Modulation (LFM). This paper deals with the design to develop and simulate pulse compression and matched filter algorithm in MATLAB to study the LFM pulse compression technique. Matched filter is used as the pulse compression filter which provides high SNR at the output. Matched Filter is mathematically equivalent to convolving the received signal with a conjugated time-reversed version of the reference signal. The main application of pulse compression Radars includes tracking of launch vehicles, unwanted particles in space, Missile guidance etc. Here, in this paper we are discussing the pulse compression application in tracking the launch vehicle so as to check whether it had followed the predetermined path or not.