## Properties of the Exponential Fourier Transform

The exponential fourier transform is linear.

IfthenThis is more a property of the linearity of integration than a property specific to the fourier transform.

The fourier transform possesses the translation property.

Letthen

Proof:

Make the substitution thenandso

And the frequency shift property. LetThen

Proof:

And the scaling property: LetThen

Proof:

Make the substitutionthenso

And the derivative property: LetThen