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Concept
Multidimensional signal processing
Summary
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 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. In some cases, m-D signals and systems can be simplified into single dimension signal processing methods, if the considered systems are separable.
Typically, multidimensional signal processing is directly associated with digital signal processing because its complexity warrants the use of computer modelling and computation. A multidimensional signal is similar to a single dimensional signal as far as manipulations that can be performed, such as sampling, Fourier analysis, and filtering. The actual computations of these manipulations grow with the number of dimensions.
Multidimensional sampling
Multidimensional sampling requires different analysis than typical 1-D sampling. Single dimension sampling is executed by selecting points along a continuous line and storing the values of this data stream. In the case of multidimensional sampling, the data is selected utilizing a lattice, which is a "pattern" based on the sampling vectors of the m-D data set. These vectors can be single dimensional or multidimensional depending on the data and the application.
Multidimensional sampling is similar to classical sampling as it must adhere to the Nyquist–Shannon sampling theorem. It is affected by aliasing and considerations must be made for eventual Multidimensional Signal Reconstruction.
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