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Automatic Visual Inspection
Published in K. S. Fu, Pattern Recognition, 2019
An alternative to the direct processing of the image is to subject it to a two-dimensional transformation, usually a Fourier or Walsh function-based transform. In some cases, the desired inspection information may be obtained from a single coefficient of the transform. More generally, a linear or other combination of several transform coefficients will be needed to allow a decision to be made. Transforms are treated in a general way by Rosenfeld and Kak,66 while the paper by Wilder67 details the solution of a particular problem by this technique.
The Discrete Cosine Transform
Published in Humberto Ochoa-Domínguez, K. R. Rao, Discrete Cosine Transform, 2019
Humberto Ochoa-Domínguez, K. R. Rao
The Walsh–Hadamard transform (WHT) [178, 234, 495]Walsh-Hadamard transform is known to be fast since the computation involves no multiplications. Thus, an algorithm for DCTDCT via WHT may well utilize this advantage. The WHTWHT is a suboptimal, real, orthogonal transform that projects a signal into rectangular waveforms called Walsh functionsWalsh functions. The functions have only two values, +1 or −1.
Third-Generation Cellular Communications: An Air Interface Overview
Published in Jerry D. Gibson, Mobile Communications Handbook, 2017
Walsh functions are generally the preferred basis for orthogonal modulation. Walsh functions are derived from the rows of Walsh matrices (also known as Walsh–Hadamard matrices). These matrices are square matrices whose dimensions are 2r by 2r, where r is a nonnegative integer. Assume that the N by N Walsh matrix is denoted as HN. Then the first two Walsh matrices in the series {H1, H2, H4, …} are
Hardware-Based Novel Applications to Locate Faults in Branched Distribution Systems
Published in Electric Power Components and Systems, 2023
Hatice Okumus, Fatih Mehmet Nuroglu
The obtained detailed coefficients are then passed through FWHT transform. FWHT is a high-speed variation of the Walsh–Hadamard Transform [25]. It divides the input signal into a series of rectangular, orthogonal waveforms, known as Walsh functions, consisting of values that are either 1 or −1. The FWHT transform of a matrix can be defined as in (3);
Electroencephalography applied compression algorithms qualitative analysis
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2020
Aratã Andrade Saraiva, Felipe Miranda de Jesus Castro, Renato Conceição Nascimento, Rodrigo Teixeira de Melo, José Vigno Moura Sousa, Antonio Valente, Nuno Miguel Fonseca Ferreira
The WHT is a lossy non-sinusoidal, orthogonal transformation technique that decomposes the signal into a series of base functions, these base functions are called Walsh functions, which are rectangular and square waves with values of −1 and 1. They are also known as Hadamard, Walsh, or Walsh Fourier transform.