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The National Science Foundation
ME 437 The National Science Foundation
 Engineering Mathematics
Special Functions | Differential Equations | Fourier Series | Laplace Transforms | Probability and Random Processes | Linear Systems | Useful Integrals | Vector Identities

Fourier Series

Summary of Fourier Transform Properties

Consider the Fourier Exponential Series in the region

Replacing the expression for the coefficient

In the last step we have defined

As

Define Fourier Transform (Exponential)

The inverse transform is

The above two equations are a Fourier Exponential Transform Pair.

Fourier Integral Representation (FIR) may be restated as

or

For even functions (i.e.

Definition: Fourier-Cos Transform Pair:

For odd functions (i.e.

Definition: Fourier-Sin Transform Pair:

Dr. Goodarz Ahmadi | Turbulence & Multiphase Fluid Flow Laboratory | Department of Mechanical & Aeronautical Engineering
Copyright © 2002-2005 Dr. Goodarz Ahmadi. All rights reserved.
Potsdam, New York, 13699
ahmadi@clarkson.edu