Conjugate Symmetry

For many LTI systems of interest, the response to a real valued input signal must itself be real valued. As we will see, this implies that the transfer function must have conjugate symmetry:

where the complex variable is identified with for continuous time systems and with for discrete time systems, and denotes the complex conjugate of .

• Proof of Conjugate Symmetry for Continuous Time
• Proof of Conjugate Symmetry for Discrete Time