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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] |
