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In [[signal processing]], '''multidimensional signal processing''' covers all signal processing done using [[multidimensional sampling]]. 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. Specifically, useful data is sampled in more than one dimension, such that multiple sensors are used to construct the data set. Examples of this are [[image processing]] and multi-sensor radar detection. Both of these examples use multiple sensors to sample signals in adjacent space and form images based on the manipulation of these multiple signals.
Multidimensional signals are part of [[multidimensional systems]], and as such are generally more complex than classical, single dimension signal processing. Processing in multi-dimension (m-D) requires more complex algorithms to handle calculations such as the [[Fast Fourier Transform]] due to more degrees of freedom<ref name="dudmer83">D. Dudgeon and R. Mersereau, Multidimensional Digital Signal Processing, Prentice-Hall, First Edition, pp. 2, 1983.</ref>. In some cases, m-D signals and systems can be simplified into single dimension signal processing methods, utilizing assumptions such as symmetry.
Typically, multidimensional signal processing is directly associated with [[digital signal processing]] because its complexity warrants the use of computer modelling and computation<ref name="dudmer83"/>. A multidimensional signal is similar to a single dimensional signal as far as manipulations that can be performed, such as [[Sampling (signal processing)|sampling]], [[Fourier analysis]], and [[Filter (signal processing)|filtering]]. The actual computations of these manipulations grow with the number of dimensions.
== Sampling ==
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{{main|Filter (signal processing)}}
[[File:2-D filter frequency response and 1-D filter prototype frequency response.gif|thumb|500px|right|A 2-D filter (left) defined by its 1-D prototype function (right) and a mapping function.]]
Filtering is an important part of any signal processing application. Similar to typical single dimension signal processing applications, there are varying degrees of complexity within filter design for a given system. M-D systems utilize [[digital filters]] in many different applications. The actual implementation of these m-D filters can pose a design problem depending on whether the multidimensional polynomial is factorable<ref name="dudmer83_2"/>. Typically, a [[prototype]] filter is designed in a single dimension and that filter is [[extrapolate|extrapolated]] to m-D using a [[map (mathematics)|mapping function]]<ref name="dudmer83_2"/>. One of the original mapping functions from 1-D to 2-D was the McClellan Transform <ref name="mer78">Mersereau, R.M.; Mecklenbrauker, W.; Quatieri, T., Jr., "McClellan transformations for two-dimensional digital filtering-Part I: Design," Circuits and Systems, IEEE Transactions on , vol.23, no.7, pp.405,414, Jul 1976.<ref/>. Both [[FIR]] and [[IIR]] filters can be utilized in this manner, depending on the application.
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