Optimization of Three-Dimensional Nonrecursive Digital Walsh Domain Filters

Abstract

As known, the three-dimensional (3-D) nonrecursive digital filtering is a computational process by which a 3-D digital input signal (sequence of samples) is transformed into a 3-D digital output signal. The output samples of such a filter are determined as weighted sums of past and present input samples. This type filtering process can be implemented by other transformations than the well-known Fourier transformation. Among many transformations,special role plays the 3-D Walsh transformation, which is based on the 3-D Walsh functions [1]. The 3-D Walsh functions are two-valued functions, only taking the two values +1 or −1. Therefore, the 3-D Walsh transform can be computed much faster than the 3-D Fourier transform.