Differentiation and Fourier Transforms
One reason the Fourier transform is so important in many applications is that it can convert expressions involving derivatives of unknown functions to simpler algebraic expressions. We will derive the main formulas for this conversion immediately below and then spend most of the rest of this chapter discussing some of the results that follow directly from these formulas.
22.1 The Differentiation Identities Initial Derivations
Deriving the main identities of this chapter is fairly straightforward if we use the integral formulas and make a few “reasonable” assumptions. Later, we will look a little more closely at these assumptions and derivations.
Two derivations will be presented. In both, f and ...
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