ABSTRACT
The answer to this question is yes, at least for “most practical cases”. The formula is the convolution formula, and this chapter is a study of that formula.
24.1 Derivation of the Convolution Formula We will derive the convolution formula by attempting to evaluate F −1[FG]|t in terms of f and g (where, as usual, f = F −1[F] and g = F −1[G] ). For this derivation, we will assume both f and G are in A so that we can use the integral formulas for their transforms,
F(ω) = ∫ ∞
−∞ f (s) e−i2pisω ds and g(τ ) =
G(ω) ei2piωτ dω .
