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.TXT 2 28 332 0
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{\plain Computing Centered 2-D Fourier Transforms}
}
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{\plain Ken Castleman}
}
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{\plain DFT{}{_10}{.MCD, 12/28/95}}
}
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.TXT 6 -64 335 0
Cg a85.375000,86.500000,220
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{\plain The DFT will compute an MTF from
 an FIR, but it requires an awkward arrangement
 of the elements in the FIR and MTF matrices.
 The centered DFT formulation used here 
allows the functions to be centered in their
 matrices.}
}
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Cg a43.625000,86.375000,61
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{\plain {Suppose the desired MTF, given 
as a 5x5 spectrum matrix is}}
}
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{\plain {The 2}{-D inverse centered DFT 
computes an NxN-point }{convolution kernel}{
 from an NxN-point}{ transfer function}{.
 With this formulation, both the FIR and
 the MTF are centered in their matrices.}}
}
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.TXT 8 -14 322 0
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{\plain {The}{ 5x5 kernel is:}}
}
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{\plain Since F(0) = 1, t{he kernel weights
 add up to one:}}
}
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{\plain The forward centered DFT computes
 the MTF from the kernel:}
}
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.TXT 3 -56 337 0
Cg a28.750000,85.500000,112
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{\plain DFT - { Discrete Fourier Transform}\par 
FIR - Finite Impulse Response (kernel)\par 
MTF - Modulation Transfer Function}
}