Functional analysis using Walsh Functions

Functional analysis usually implies representing a signal by a series of sine-cosine functions, but is actually included in the much broader problem of decomposition, that is, separating an arbitrary signal into preferred component signals. The most common approach to decomposition still uses a complete orthogonal set of functions, such as sine-cosine functions or Bessel functions, and an integral transform. In recent years, much attention has been given to a relatively unknown set of orthogonal functions, the Walsh Functions. A general discussion of orthogonal functions and series expansion, and some of the properties of Walsh Functions are presented followed by the necessary theory to determine the component coefficients of linearly composed signals. The theory employs an integral transformation utilizing Walsh Functions and a matrix transformation yielding a least-square-fit approximation. Two particular problems investigated are harmonic analysis and analysis of signals composed of nonorthogonal components. A computer simulation studies accuracy for different parameters. A description of a Walsh Function generator, integral transform devices, and a matrix multiplier designed and built is given. Conclusions are drawn regarding the limitations and applications of the system.Electrical and Computer Engineering, Department o