Motivation
Hermitian functions appear frequently in mathematics, physics, and signal processing. For example, the following two statements follows from basic properties of the Fourier transform:
- The function is real-valued if and only if the Fourier transform of is Hermitian.
- The function is Hermitian if and only if the Fourier transform of is real-valued.
Since the Fourier transform of a real signal is guaranteed to be Hermitian, it can be compressed using the Hermitian even/odd symmetry. This, for example, allows the discrete Fourier transform of a signal (which is in general complex) to be stored in the same space as the original real signal.
- If f is Hermitian, then
Where the is cross-correlation, and is convolution.
- If both f and g are Hermitian, then, which in general is not true.
Read more about this topic: Hermitian Function
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