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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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