Discussion of Aliasing

It is a property of Fourier transform mathematics that multiplication in one domain is equivalent to convolution in the other. (Convolution has already been introduced with regard to apodization in Section 2.3.) If we sample an analog interferogram at constant intervals of retardation, we have in effect multiplied the interferogram by a repetitive impulse function. The repetitive impulse function is in actuality an infinite series of Dirac delta functions spaced at an interval 1 jx. That is, 

This process is illustrated in Eigure 3.5. Eigure 3.5a shows a discretely sampled sinc function sampled at a retardation of (2Vniax) and Eigure 3.5b shows its Eourier transform. As can be seen clearly, there is no overlap of the resulting spectra (triangular functions, in this case). If the sampling frequency were decreased so that 

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