LMS algorithm and discrete orthogonal transforms

A general relation between the least mean square (LMS) algorithm and the discrete orthogonal transforms is established. Discrete orthogonal transforms, including the discrete Fourier transform (DFT), the discrete Hartley transform (DHT), the discrete cosine transform (DCT), the discrete sine transform (DST), and the Walsh-Hadamard transform (WHT), etc. are extensively used in signal and image processing. It is shown that the LMS algorithm could provide a means for the calculation of forward orthogonal transforms as well as inverse orthogonal transforms by properly choosing the input vector and adaptation speed.<>