Fourier and wavelet analysis of sperm whale acoustic data in the northern Gulf of Mexico

The Fourier wavelet based regularized deconvolution (ForWaRD) algorithm is a combination of Fourier deconvolution and wavelet denoising originally proposed by [15] and modified by [8]. The research described here uses the ForWaRD algorithm with recent broadband underwater acoustic data from sperm whales acquired in the northern Gulf of Mexico (GoM). Several modifications were required for the algorithm to yield the best results. Applying wavelet denoising and Fourier deconvolution allows smoothing of the data and separating the signal from the impulse response. Results indicate that the modification of using deconvolution techniques other than Wiener deconvolution improves the performance of the ForWaRD algorithm with underwater acoustic data. Other modifications made to the type of wavelet thresholding as well as the wavelet choice for wavelet decomposition greatly improve the error in reconstruction of the signal.