# Orthogonal Transforms for Digital Signal Processing

@article{Rao1979OrthogonalTF, title={Orthogonal Transforms for Digital Signal Processing}, author={Kamisetty Ramamohan Rao and Nasir Ahmed}, journal={IEEE Transactions on Systems, Man, and Cybernetics}, year={1979}, volume={9}, pages={66-67} }

A tutorial-review paper on discrete orthogonal transforms and their applications in digital signal and image (both monochrome and color) processing is presented. [... ] Key Method Efficient algorithms for fast implementation of these transforms based on matrix partitioning or matrix factoring are presented. Expand

## 773 Citations

Multichannel transforms for signal/image processing

- Computer Science, EngineeringIEEE Trans. Image Process.
- 1996

The discrete-time one-dimensional multichannel transforms proposed in this paper are related to two-dimensional single-channel transforms, notably to the discrete Fourier transform (DFT) and to the DHT.

Transform Coding of Signals with Bounded Finite Differences: from Fourier to Walsh, to Wavelets

- Computer Science
- 2001

A unified approach is presented for deriving upper bounds of spectra of orthogonal transforms on classes of input signals with bounded first and second order finite differences to select the significant transform coefficient packets a priori and compute the maxima of mean-square errors of reconstruction for a given compression ratio.

Orthogonal Discrete Fourier and Cosine Matrices for Signal Processing

- Computer Science
- 2011

Interestingly, the Reverse Jacket Transform(RJT) matrix has a strong geometric structure that reveals a circulant expansion and contraction properties from a basic 2x2 sparse matrix.

Transform-domain adaptive filters: an analytical approach

- Computer ScienceIEEE Trans. Signal Process.
- 1995

The effects of the preprocessing performed in DFT-L MS and DCT-LMS for first-order Markov inputs are analyzed and it is shown that for Markov-1 inputs of correlation parameter /spl rho//spl isin/[0,1], the eigenvalue spread after DFT and power normalization tends to (1+/ spl rho/)l as the size of the filter gets large.

USING OF DISCRETE ORTHOGONAL TRANSFORMS FOR CONVOLUTION

- Computer Science
- 2002

This paper presents a convolution formula for some selected discrete orthogonal transforms (DOT) and shows how to compute convolution using LaSalle's inequality.

Discrete Orthogonal Multi-transform on Chip (DOMoC)

- Computer Science
- 2019

Two kinds of architectures to perform multiple N-point 1D-discrete orthogonal transforms on single chip are proposed, FFT parallel architecture based and matrix-vector multiplier based.

Upper bounds of wavelet spectra on the class of discrete Lipschitzian signals

- Computer ScienceOptics & Photonics
- 1996

These estimates allow not only to a priori select the wavelet coefficient packets that have minimum input in signal reconstruction, but also to compute the maximum mean-square errors of reconstruction for a particular compression ratio and to analyze efficacy of different wavelets based on that criterion.

The Haar-Wavelet Transform in Digital Image Processing: Its Status and Achievements

- Computer Science, Mathematics
- 2004

It is presented that two-dimensional both, the Haar and wavelets functions products man be treated as extractors of particular image features and shown that some coefficients from both spectra are proportional, which s slightly computations and analyses.

A Multiparametric Class of Low-complexity Transforms for Image and Video Coding

- Computer ScienceSignal Process.
- 2020