Fourier’s theorem is an elegant mathematical transformation that has demonstrated its significant worth after being applied to countless physical scenarios. The examples in Chapter 2 explored the Fourier series expansion of a mathematical function f(t) that might represent a time-varying “analog” signal. In the laboratory or in the field, signals are produced by physical systems, and the goal may be to learn something about the physical system by exploring the signal’s frequency content. Instead of describing the signal with a mathematical function, the signal’s state is measured at selected points in time, such as with transducers and data-acquisition equipment. The result is a sequence of measurements where each value represents a sample of the continuous signal of interest at a given time; such data is referred to as time-series data. In order to explore the frequency content of the underlying signal based on the sample data, instead of finding the frequency content of a mathematical function, as in Chapter 2, one must perform an analogous operation with a series of discretely sampled points. Fourier transform methods can be adapted to analyze the frequency content of time-series data.
You have requested a machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Neither SPIE nor the owners and publishers of the content make, and they explicitly disclaim, any express or implied representations or warranties of any kind, including, without limitation, representations and warranties as to the functionality of the translation feature or the accuracy or completeness of the translations.
Translations are not retained in our system. Your use of this feature and the translations is subject to all use restrictions contained in the Terms and Conditions of Use of the SPIE website.
Fourier Transforms for Discretely Sampled Data