Redundancy of signals and transformations and computational complexity of signal and image processing

We demonstrate the use of informational redundancy of signals and transforms for reducing the computational costs of signal processing. Four concrete examples of accelerated signal processing algorithms are presented to support the idea of purposive use of signal and transform redundancy for saving the computational costs. These are: an accelerated algorithm for Fourier spectral analysis, an accelerated algorithm for computing the signal local histograms, the quantized discrete Fourier transforms, and recursive implementation of arbitrary digital filters. The former two reduce computation time by exploiting signal redundancy. The latter two save processing time at the expense of the accuracy of representation of the corresponding signal transforms