FPGA Realizations of Walsh Transforms for Different Transform and Word lengths into Xilinx and Altera Chips

Abstract

This paper presents FPGA realizations of Walsh transforms. The realizations are targetted for the system of arbitrary waveform generation, addition/ subtraction, multiplication, and processing of several signals based on Walsh transforms which is defined in term products of Rademacher functions. Input signals are passing through the system in serial, the output either signals or coefficients are also passing out in serial. To minimize the area utilization when the systems are realized in FPGA chips, the word lengths of every processing step have been designed carefully. Based on this, FPGA realizations of those various applications into Xilinx and Altera chips have been done. In Xilinx realizations, Xilinx ISE was used to display the results and to extract some critical parameters such as speed and static power. Meanwhile, the realizations into Altera chips have been conducted using Quartus. Comparisons of speed and power among Xilinx and Altera chip realizations are presented here even though this is not an apple to apple comparison. Finally, it can be concluded that Walsh transforms can be realized not only for the applications that have been done here, but it is potential can be used for other applications.