Comparing noise removal in the wavelet and Fourier domains

This paper compares time series decomposition in the frequency domain via the discrete Fourier transform to time series decomposition in the wavelet domain via the Wavelet transform for the purpose of signal smoothing and noise removal. The information cost of the signal is computed as a predictor of the performance of the filtering process. Simulations are conducted comparing the frequency domain filter to wavelet domain filters on a variety of signals corrupted with additive Gaussian noise.