Several applications in radar systems entail low range side lobe performance to identify the targets. It is achieved by pulse compression processing. The chirp signal also known as linear frequency modulation (LFM) signal is most widely used for this purpose. Since it exhibits high first side-lobe value in the autocorrelation, non linear chirp signals (NLFM) are introduced as a solution to suppress the sidelobes. NLFM signals can be generated by using simple two-stage piece wise linear frequency modulation (PWLFM) functions. The chirp rates of the two stages are selected differently. This NLFM signal exhibited better peak to sidelobe level (PSLR) values compared to its counterpart LFM signal. In this paper we present a complete contour map of the computed side lobe values, to identify the optimum chirp rates of the two stages. The side lobes are computed based on algorithm written in python scripting language. This map helped us to identify two interwoven fluctuations in the spectrum of side-lobe values that can be used to decide the breakpoint value for a given bandwidth and pulse width. The best NLFM is generated by identifying the optimum slopes of the two LFM stages, which is further combined with the windows functions to achieve a significant reduction in PSLR.