A lot of applications in radar systems necessitate low range side-lobe performance which is achieved by pulse compression processing. Linear Frequency Modulation (LFM) signal is mainly used chirp signal for this processing. The paramount drawback in LFM is the first side-lobe level of -13dB at the receiver side. In this paper, LFM signal is modified by using simple two-stage piece wise linear frequency modulation (PWLFM) functions. The autocorrelation function of this PWLFM signal exhibited low peak sidelobe level ratio (PSLR) value compared to its counterpart LFM signal. An attempt is made to further reduce the side lobe values by using novel Convolutional windows. The simulation results confirm a significant side lobe reduction by the LFM signal designed using PWLFM functions when a more flexible Power of Cosine window function is applied compared to all other window functions.