User:Tjhuston225/Multidimensional Signal Processing: Difference between revisions

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In [[digital signal processing]], '''multidimensional signal processing''' covers all signal processing done using [[multidimensional sampling]]. While multidimensional signal processing is a subset of digital 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. Examples of this are [[image processing]] and multi-sensor radar detection.

Multidimensional signals are part of [[multidimensional systems]], and as such are generally more complex than classical, single dimension signal processing. Processing in m-D (multi-dimension) requires more complex algorithms to handle calculations such as the [[Fast Fourier Transform]] due to more degrees of freedom <ref name="petmid62dudmer83">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.

== Sampling ==

{{main|Multidimensional sampling}}

Multidimensional sampling requires different analysis than typical 1-D sampling. Single dimension sampling is executing 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]]. This, latticewhich is a "pattern" based on the sampling [[vectorsvector (mathematics and physics)|vector]] of the m-D data set <ref name="mer83"> Mersereau, R.; Speake, T., "The processing of periodically sampled multidimensional signals," Acoustics, Speech and Signal Processing, IEEE Transactions on , vol.31, no.1, pp.188,194, Feb 1983.</ref>. 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 reconstruction.

== Filtering ==

{{main|filterFilter (signalSignal processingProcessing)|filter}}