Application of Calculus using a Fast Fourier Transform When Analyzing Data

by Alexander Goodchild

Submitted : Spring 2019

In this new day and age of computing and the use of these computers to measure and record data, the process in which computers analyze this data is crucial in understanding the accuracy of the digital instruments and measurements we use to gather analog information about our environment. An analog signal is a signal that consists of an infinite set of the continuous data point with an infinite set of continuous values. Digital systems, in contrast to analog, represents a continuous set of real numbers with a continuous set of values. Therefore, to transfer an analog data set into a digital one, some of the data points are “ignored” so the digital system can analyze the information. What type of accuracy can be expected when different sampling conditions and interpolation to replicate these analog signals after they have been digitized?

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