Inside Collection (Textbook): Signals, Systems, and Society

Summary: Looks at some of the consequences of conjugate symmetry of the Fourier transform of real signals.

When *conjugate symmetry*,

where the second equality uses the definition of a Riemann integral as the limiting case of a summation, and the fact that the complex conjugate of a sum is equal to the sum of the complex conjugates. The third equality used the fact that the complex conjugate of a product is equal to the product of complex conjugates.

Letting

and

Equating Equation 2 and Equation 3 gives

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