In this brief, we propose a low complexity VLSI architecture design Methodology for Wigner Ville Distribution (WVD) computation. The proposed methodology performs both auto and cross WVD computations using only the half number of Fast Fourier transform (FFT) computations as opposed to the state of the art methodologies. The FPGA implementation for proposed methodology was performed for 16 bit fixed point and 32 bit single precision floating point numbers on the Xilinx Virtex-7 FPGA (XC7vx485tffg). The proposed methodology saves 49% energy consumption when compared with the state of the art methodology. However it can be noted that the proposed methodology is independent of the VLSI implementation platform and technology node. © 2004-2012 IEEE.