 This can be particularly appealing for high-order filters because the various Fast Fourier transform algorithms permit the efficient evaluation of the DFT.The general form of DFT for multidimensional signals can be seen below, where formula_72 is periodicity matrix, formula_73 is the multidimensional signal in the space domain, formula_74 is the DFT of formula_73 in frequency domain, formula_76 is a region containing |formula_77| samples in formula_78 domain, and formula_79 is a region containing |formula_80| (formula_81) frequency samples.formula_82

Let formula_83 be the linear convolution of a finite-extent sequence formula_84 with the impulse response formula_85 of an FIR filter.