Higher-order spectra computation using wavelet transform

It has been a desire of a design engineer to combine various tools of analysis and apply them on one problem at hand. In this paper, we propose an algorithm that combines two signal processing analysis tools: higher-order spectral analysis and wavelets. The computation of polyspectra using conventional approaches involves the use of FFT algorithm. It has been shown that discrete Fourier transform (DFT) can be implemented by a fast algorithm using wavelets. By using this algorithm, polyspectra computational complexity for a certain class of signals reduces to lesser number of computations. In actual implementation, the wavelets in use have to be carefully chosen to balance the benefit of pruning of insignificant data and the price of the transform. Clearly, the optimal choice depends on the class of the data we would encounter. In this paper, we, first, present an introduction of higher-order spectral analysis. Then we discuss wavelet-based fast implementation of DFT and its importance from higher-order spectral analysis viewpoint. Finally, we develop wavelet-based algorithm for computation of polyspectra followed by conclusions.