Chapter 2 - Signal Properties¶
Symmetry¶
Continuous-time Signals¶
Even Signals¶
A signal that exhibits symmetry about the vertical axis is called an even signal.
Mathematically, an even signal must satisfy the following condition:
Show example
A common example of an even signal is a cosine wave:
Odd Signals¶
A signal that exhibits anti-symmetry about the vertical axis is called an odd signal.
Mathematically, an odd signal must satisfy the following condition:
Show example
A common example of an even signal is a sine wave:
Discrete-time Signals¶
For discrete-time signals, we have a similar definition:
Even Signals¶
Odd Signals¶
Finite Sequences / Periodic Signals¶
A related concept for finite sequences or periodic signals is called palindromic sequences. For a finite sequence with length \(N\), or a periodic signal with period \(N\), we have the following definitions.
Palindromic Sequences¶
A sequence is palindromic and has even symmetry if:
Anti-palindromic Sequences¶
A sequence are anti-palindromic and has odd symmetry if:
Conjugate Symmetry / Hermitian Functions¶
For complex signals, we also have a similar property. A complex valued function is hermitian and signal is conjugate symmetric if we have:
where the \(*\) operator denotes the complex conjugate.
Show example
A common example of a complex conjugate signal is a complex exponential.