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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
Orthogonal functions are necessary for transforms such as the FFT, or the DCT. orthogonal transform a transform whose basis functions are orthogonal. The transform matrix of a discrete orthogonal transform is an orthogonal matrix. Sometimes orthogonal transform is used to refer to a unitary transform. Orthogonal real transforms exhibit the property of energy conservation. orthogonal wavelet wavelet functions that form orthogonal basis by translation and dilation of a mother wavelet. orthographic projection a form of projection in which the rays forming an image are modeled as moving along parallel paths on their way to the image plane: usually the paths are taken to be orthogonal to the image plane. Orthographic projection suppresses information on depth in the scene. A limiting case of perspective projection. orthonormal functions an orthogonal signal set f m (t) on [t1 , t2 ] such that
Optical Computing
Published in Toyohiko Yatagai, Fourier Theory in Optics and Optical Information Processing, 2022
which is called a wavelet. As shown in Fig. 8.21, wavelets are similar to each other. As compared with the Fourier transform, the parameter a in the wavelet corresponds to the period, inverse of the frequency, but the position parameter b has no corresponding parameter in the Fourier transform. The wavelet transform is defined using kernels of a series of wavelets. Wavelet transforms with continuous parameters a and b are called continuous wavelet transforms, and wavelet transform with discrete parameters are discrete wavelet ones. Discrete wavelet transforms with orthogonal kernels are called orthogonal wavelet transforms. Some examples of mother wavelets are shown in Fig. 8.22.
Signal Processing for EEGs
Published in Narayan Panigrahi, Saraju P. Mohanty, Brain Computer Interface, 2022
Narayan Panigrahi, Saraju P. Mohanty
Biorthogonal: Biorthogonal filters state a superset of orthogonal wavelet filters. The bi-orthogonal family wavelets are signed as bior. Bi-orthogonal wavelet transform has frequently been used in numerous image processing applications because it makes possible multi-resolution analysis and does not produce redundant information.
Establishment and application of a fractional difference-autoregressive model for daily runoff time series forecasting based on wavelet analysis
Published in Systems Science & Control Engineering, 2018
Jie Zhang, Meili Wang, JieLong Hu
The Mallat algorithm was put forward by Mallat on the basis of multiresolution analysis. It has been proved that it is suitable for the fast decomposition and reconstruction of signal by orthogonal wavelet. The Mallat fast algorithm includes the decomposition algorithm and the reconstruction algorithm. Mallat decomposition algorithm Where, H is the decomposition low pass filter, G is the decomposition high pass filter. The original time series can be decomposed into an approximation signal () and detail signals () respectively by using the above equation. Mallat reconstruction algorithm
Generation of enhanced information image using curvelet-transform-based image fusion for improving situation awareness of observer during surveillance
Published in International Journal of Image and Data Fusion, 2019
Wavelet-transform-based technique is a form of multi-resolution transform in which the image is decomposed using filter banks to extract coarse and detailed coefficients of an image at every level. These extracted coefficients are then fused using specific fusion rules. The fused coefficients are then rearranged to form a matrix as per their level and fused image is reconstructed using another reconstruction filter bank. The orthogonal wavelet technique makes use of same filter bank for decomposition and reconstruction. However, biorthogonal wavelet families use separate decomposition and reconstruction filters.
Audio Watermarking with Multiple Images as Watermarks
Published in IETE Journal of Education, 2020
Amita Singha, Muhammad Ahsan Ullah
In wavelet analysis, the Discrete Wavelet Transform (DWT) decomposes a signal into a set of mutually orthogonal wavelet basis functions. These functions differ from sinusoidal basis functions in that they are spatially localized – that is, nonzero over only part of the total signal length. Furthermore, wavelet functions are dilated, translated, and scaled versions of a common function, known as the mother wavelet. As is the case in Fourier analysis, the DWT is invertible, so that the original signal can be completely recovered from its DWT representation.