Hermitian function
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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:
for all 
in the domain of definition of 
.
is the complex conjugate of 
.
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 
in the domain of definition of .
From this definition follows immediately that is a Hermitian function, then
- the real part of is an even function
- the imaginary part of is an odd function
[edit] Motivation
Hermitian functions appear frequently in mathematics and signal processing. As an example, the following statements are important when dealing with Fourier transforms:
- The function is real-valued
the Fourier transform of is Hermitian.
- The function is Hermitian the Fourier transform of is real-valued.
