where the fundamental spatial frequency is us = 2n/X r /mm 5.2-10
The complex-form Fourier coefficients are given by
Thus the complex Fourier series for the pulse train is
The sampler output, g*(x), is the space-domain product of Equation 5.2-12 and g(x):
Now the Fourier transform theorem for complex exponentiation is
Using this theorem, one can write the Fourier transform of the ideally sampled image as
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