Performance and computation ranking of fast unitary transforms in applications

For several signal processing applications, the usefulness of Fast Unitary Transforms (FUT) is now well recognized [1-7]. For signal representation, filtering and encoding, it is well known that the Karhunen-Loeve (KL) Transform, based on signal statistics, is optimum in various senses, but the KL Transform is slow. Suboptimum FUT's allow a trade-off between performance and speed. In this paper, we compare and rank the KL, Fourier, Walsh-Hadamard, Haar, Discrete Cosine, Slant Walsh Hadamard and Slant Haar Transforms by their performance in applications and by the number of elementary operations they require. In encoding and filtering, recursive techniques are widely used and are generally fast. By considering both performance and computations we are able to compare directly recursive and transform algorithms. The comparison brings to light a performance versus computation bound for the two classes of processing techniques.