# Fourier transform of function times periodic function

#### aaaa202

Suppose I have a function of the type:

h(t) = g(t)f(t)

where g(t) is a periodic function. Are there any nice properties relating to the fourier transform of such a product?

Edit: If not then what about if g(t) is taken as the complex exponential?

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#### DrClaude

Mentor
$$h(t) \Leftrightarrow H(f)$$
is a transform pair, then
$$h(t) e^{-2 \pi i f_0 t} \Leftrightarrow H(f - f_0)$$
and its called frequency shifting (taken from Numerical Recipes in C).

"Fourier transform of function times periodic function"

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