tags: ece-402
Fourier Inversion Theorem
The Fourier inversion theorem states that it is possible to recover a function from its [Fourier transform].
Intuitively: if we know all frequency and phase information about a wave, then we can reconstruct the original wave precisely.
Application
The application of the Fourier inversion theorem is very common through this basic strategy:
- apply the Fourier transform on a signal
- perform some operation or simplification on the Fourier transform
- apply the inverse Fourier transform to obtain a modified version of the original signal
Sound
Applying the Fourier inverse theorem in sound and audio relies on the above basic strategy. For ex:
- identifying unwanted [frequencies] in a [dry signal] using Fourier transform, removing those unwanted frequencies with [EQ], and applying inverse Fourier transform to obtain the wet signal