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.TXT 2 30 273 0
Cg a26.125000,66.375000,35
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{\plain {Small Kernel from Subsampled MTF}}
}
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{\plain {F_16-13}{.MCD, 12/19/94}}
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{\plain {The }{1-D Discrete Fourier Transform
 computes an M-point}{ transfer function}{
 from an M-point}{ impulse response}{:}}
}
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{\plain {Suppose the desired Gaussian TF,
 given as an N-point spectrum vector centered
 on element b, is}}
}
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{\plain {whose N-point FIR is:}}
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{\plain {We set up an M-point TF by subsampling
 G:}}
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{\plain {Then its M-point FIR centered on
 element a is}}
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({0:f}NAME)[({0:n}NAME):((1)/(\({0:M}NAME)))*((0,{0:M}NAME-1,{0:m}NAME,({0:F}NAME)[({0:m}NAME)*{0:exp}NAME({0:j}NAME*2*{0:\p}NAME*({0:n}NAME-{0:a}NAME)*({0:m}NAME-{0:a}NAME)/({0:M}NAME))){64})
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{\plain {We can}{ transform this back to
 an N-point spectrum, to see}{ the approximation
 TF}{:}}
}
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{\plain {If an M-point function is centered
 on element a, and we want its N-point spectrum
 centered on element b, we can use:}}
}
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{\plain {where}}
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(1)/(\({0:M}NAME))*({0:f}NAME){51}={0}?_n_u_l_l_
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{\plain {and the MSE of the approximation
 is:}}
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{0:RMSE}NAME={148583}?_n_u_l_l_
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Cg a9.375000,26.500000,13
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{\plain Figure 16-13}
}