Computation of Time-Varying Cross-Spectra by Harmonic Wavelets
David E. Newland · 2001
Abstract Harmonic wavelets provide an organised method for local computations of the cross-spectra between two signals. Each signal is analysed into its wavelet expansion. The product of the (complex) amplitudes of corresponding terms in each expansion is then a measure of the time varying cross-spectral density between the two signals. To ensure adequate discrimination at low frequencies, it is necessary introduce additional terms into the expansion by intentionally oversampling, but the principle remains unchanged and the method allows the amplitude and phase of time-varying cross-spectra to be identified at closely-spaced time intervals. Some examples illustrate the procedure, which can be programmed simply using an FFT algorithm.