Article,
New Method of Signal Denoising by the Paired Transform
Applied Mathematics and Sciences: An International Journal (MathSJ), 1 (2): 01-20 (August 2014)
Abstract
A parallel restoration procedure obtained through a splitting of the signal into multiple signals by the paired transform is described. The set of frequency-points is divided by disjoint subsets, and on each of these subsets, the linear filtration is performed separately. The method of optimal Wiener filtration of the noisy signal is considered. In such splitting, the optimal filter is defined as a set of sub filters applied on the splitting-signals. Two new models of filtration are described. In the first model, the traditional filtration is reduced to the processing separately the splitting-signals by the shifted discrete Fourier transforms (DFTs). In the second model, the not shifted DFTs are used over the splitting-signals and sub filters are applied. Such simplified model for splitting the filtration allows for saving 2N − 4(r + 1) operations of complex multiplication, for the signals of length N = 2^r, r > 2.
