Hermitian function

In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: (where the

In physics, this property is referred to as PT symmetry.

This definition extends also to functions of two or more variables, e.g., in the case that

is a function of two variables it is Hermitian if for all pairs

From this definition it follows immediately that:

is a Hermitian function if and only if Hermitian functions appear frequently in mathematics, physics, and signal processing.

For example, the following two statements follow from basic properties of the Fourier transform:[citation needed] 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.