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In engineering and scientific problems one of the most commonly used tools is Fourier analysis. With the increasing availability of analog, hybrid, and digital computers, it is useful to examine special techniques applicable to these machines. This paper presents: 1) methods for evaluating the required integrals on either a digital or an analog computer and 2) an analysis which results in guidelines for choosing the sampling interval when the problem is done digitally. Parts of the material presented in this paper can be found in other sources although there are some refinements included here that make the implementation of the theory considerably easier. The theory is valid for any machine, but minor modifications may have to be made in hybrid computer patching or in the digital program to conform with equipment restrictions.