Access to eBooks is limited to institutions that have purchased or currently subscribe to the SPIE eBooks program. eBooks are not available via an individual subscription. SPIE books (print and digital) may be purchased individually on SPIE.Org.

Contact your librarian to recommend SPIE eBooks for your organization.
Chapter 3:
Fourier Transforms for Discretely Sampled Data
Abstract

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.

Online access to SPIE eBooks is limited to subscribing institutions.
CHAPTER 3
40 PAGES


SHARE
Back to Top