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Wavelet For Multidimensional Signals Analysis
Wavelets are often used to analyse piece-wise smooth signals. Wavelet coefficients can efficiently represent a signal which has led to data compression algorithms using wavelets. Wavelet analysis is extended for multidimensional signal processing as well. This article introduces a few methods for wavelet synthesis and analysis for multidimensional signals. There also occur challenges such as directivity in multidimensional case. Multidimensional separable discrete wavelet transform (DWT) The discrete wavelet transform is extended to the multidimensional case using the tensor product of well known 1-D wavelets. In 2-D for example, the tensor product space for 2-D is decomposed into four tensor product vector spaces as This leads to the concept of multidimensional separable DWT similar in principle to the multidimensional DFT. gives the approximation coefficients and other subbands: low-high (LH) subband, high-low (HL) subband, high-high (HH) subband, give detail coeffi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many kinds of data, including audio signals and images. Sets of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multidimensional Signal Processing
In signal processing, multidimensional signal processing covers all signal processing done using multidimensional signals and systems. While multidimensional signal processing is a subset of signal processing, it is unique in the sense that it deals specifically with data that can only be adequately detailed using more than one dimension. In m-D digital signal processing, useful data is sampled in more than one dimension. Examples of this are image processing and multi-sensor radar detection. Both of these examples use multiple sensors to sample signals and form images based on the manipulation of these multiple signals. Processing in multi-dimension (m-D) requires more complex algorithms, compared to the 1-D case, to handle calculations such as the fast Fourier transform due to more degrees of freedom.D. Dudgeon and R. Mersereau, Multidimensional Digital Signal Processing, Prentice-Hall, First Edition, pp. 2, 1983. In some cases, m-D signals and systems can be simplified into single ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Wavelet Transform
In numerical analysis and functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ..., a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency ''and'' location information (location in time). Definition One level of the transform The DWT of a signal x is calculated by passing it through a series of filters. First the samples are passed through a low-pass filter with impulse response g resulting in a convolution of the two: :y[n] = (x * g)[n] = \sum\limits_^\infty The signal is also decomposed simultaneously using a high-pass filter h. The outputs give the detail coefficients (fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Product
In mathematics, the tensor product V \otimes W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of V \otimes W denoted . An element of the form v \otimes w is called the tensor product of v and w. An element of V \otimes W is a tensor, and the tensor product of two vectors is sometimes called an ''elementary tensor'' or a ''decomposable tensor''. The elementary tensors span V \otimes W in the sense that every element of V \otimes W is a sum of elementary tensors. If bases are given for V and W, a basis of V \otimes W is formed by all tensor products of a basis element of V and a basis element of W. The tensor product of two vector spaces captures the properties of all bilinear maps in the sense that a bilinear map from V\times W into another vector space Z factors uniquely through a linear map V\otimes W\to Z (see the section below ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiki Figures Mod
A wiki ( ) is a form of hypertext publication on the internet which is collaboratively edited and managed by its audience directly through a web browser. A typical wiki contains multiple pages that can either be edited by the public or limited to use within an organization for maintaining its internal knowledge base. Its name derives from the first user-editable website called "WikiWikiWeb," with "wiki" being a Hawaiian word meaning "quick." Wikis are powered by wiki software, also known as wiki engines. Being a form of content management system, these differ from other web-based systems such as blog software or static site generators in that the content is created without any defined owner or leader. Wikis have little inherent structure, allowing one to emerge according to the needs of the users. Wiki engines usually allow content to be written using a lightweight markup language and sometimes edited with the help of a rich-text editor. There are dozens of different wik ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filterbank Mod Try 2
In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal. The process of decomposition performed by the filter bank is called ''analysis'' (meaning analysis of the signal in terms of its components in each sub-band); the output of analysis is referred to as a subband signal with as many subbands as there are filters in the filter bank. The reconstruction process is called ''synthesis'', meaning reconstitution of a complete signal resulting from the filtering process. In digital signal processing, the term ''filter bank'' is also commonly applied to a bank of receivers. The difference is that receivers also down-convert the subbands to a low center frequency that can be re-sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
