Multidimensional signal processing

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.

Single dimension sampling is executed by selecting points along a continuous line and storing the values of this data stream.

[3] In general, fast Fourier transforms (FFTs), reduce the number of computations by a substantial factor.

Similar to typical single dimension signal processing applications, there are varying degrees of complexity within filter design for a given system.

The actual implementation of these m-D filters can pose a design problem depending on whether the multidimensional polynomial is factorable.

[4] Both FIR and IIR filters can be transformed to m-D, depending on the application and the mapping function.

A 2-D filter (left) defined by its 1-D prototype function (right) and a McClellan transformation.