Chapter 5

Transforms

5.1 Fourier Transform

5.1.1 Introduction

Having introduced the concept of the Fourier series in section 4.3, we will now introduce the Fourier transform. You will recall that the Fourier series is the representation of a function as a finite series of sine and cosine terms. If you look back at the definition of the individual terms in Eq. 4.24, you can see that these terms vary in two means:

 the amplitude or strength which is given by the prefactor derived from the integrals Eq. 4.26, Eq. 4.27, and Eq. 4.28

 the frequency which is given by the index n which occurs as multiplier in the sine and cosine terms

Until now we have simply calculated these terms individually. However, there may be a better option. What if there ...

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