Walsh functions for spectral analysis
Paul Sánchez · NCSU Libraries Repository (North Carolina State University Libraries) · 1983
Walsh analysis has several nice properties aside from allowing the experimenter to work with discrete parameter spaces. There is a Fast Walsh Transform (FWT) which is analogous to the Fast Fourier Transform (FFT) used in more traditional spectral computations. The FWT is like the FFT in that it requires n log2n operations to evaluate, where n is the number of observations available. However, in the case of the FWT those operations are additions or subtractions, which are substantially faster for digital computers than the complex multiplications required by the FFT. Furthermore, addition and subtraction are computationally stable operations for finite bit arithmetic, while multiplication and division are not.We will show in the oral presentation that if the error term of a stochastic system is additive discrete white noise then the Walsh spectral estimator has a x2 distribution with 2 degrees of freedom. This enables the experimenter to perform statistical tests to accept or reject the hypothesis that a spike in the spectrum is due to random fluctuation.