Picture processing: 1977

Walsh-Hadamard matrices are rearranged such that the first half of the rows represents cal functions in increasing order of sequency whereas the second half represents sal functions in decreasing order of sequency. The transform based on this rearrangement is called the Cal-Sal Walsh-Hadamard transform or (WHT) cs . General expressions for developing the elements of these matrices are developed. These matrices are decomposed into sparse matrix factors which lead directly to the fast algorithms similar to those for other forms of the WHT. The (WHT) cs is useful in mapping an even or odd sequence since, in this case, at least one-half of the transform components will be zero.

Cal-sal Walsh-Hadamard transform

The stochastic behavior of digital combinational circuits is analyzed by the use of Walsh functions. An n-input Boolean function is represented as a Walsh series and the error caused by noise is measured in terms of a distance which is the fraction of the time that the system output due to noise-corrupted signal differs from that due to signal alone. It is shown that the error can be expressed as the sum of two parts: one part depends only on noise statistics, and the other on both signal and noise. Some interesting properties of both parts are discussed and typical examples are given.

Noise-Error Determination of Combinational Circuits by Walsh Functions

This paper proposes a method to estimate the flicker severity index using the Walsh Hadamard transform (WHT). A weighting filter in the sequency domain is utilized for direct computation of the flicker index. The proposed method is compared with a flicker meter in the frequency domain that uses the fast Fourier transform (FFT). It is seen by numerical simulations that the proposed method yields flicker severity indices within the stipulated range for six test signals prescribed by the IEC. The computational simplicity of the Hadamard transform is explained with respect to floating point operations(flops). complexity of FFT increases as order of N Increases and computational savings of Hadamard transform over FFT is shown with respect to number of floating point operations through the simulations carried in MATLAB and C platforms.

Flickermeter Design: An Improved Method to evaluate Short term Flicker Severity Index (Pst) using Walsh Hadamard Transform (WHT)

In place computation of the Hadamard transform in cal-sal order

A simple algorithm is developed for obtaining the sequency vector of high-order Hadamard transform matrices without the need for converting the order of individual Hadamard functions to sequency.

An Algorithm for Sequency Ordering of Hadamard Functions

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An Algorithm for Sequency Ordering of Hadamard Functions