Ac 2007-1038: Comparing the Walsh Domain to the Fourier Domain with a Labview-based Communication Systems Toolkit

Although the Fourier Transform is the traditional frequency domain analysis tool in communications systems, other transforms are pointed out in the context of orthogonal series representation of periodic signals. Last year, we became interested in the Walsh Transform and developed virtual instruments (VIs) to compute the Walsh transform, to generate the Walsh basis functions and modified LabVIEW’s natural ordered fast Walsh Transform (FWT) routine to provide Walsh ordered Walsh transforms and a recent publication 1 reported on this expansion of the Communication Systems Toolkit into the Walsh domain. This paper will describe the utilization of these most recent tools in order to compare the Walsh domain to the Fourier domain. We will compare the basis functions in each transformation and demonstrate similarities and differences between FFT and FWT. We will then propose a new arrangement of the FWT sequency plots that will correspond to the magnitude spectrum plots obtained by the FFT. We will conclude by a summary of the student responses to exercises comparing these two transform methods.