Some Signal Classifications

Plot of a quadratic signal with time

Some signals have specific properties which makes computations simpler. For example,

Even and Odd

A signal is called even (or symmetric) if

    \begin{equation*}     s[-n] = s[n] \end{equation*}

Flipping an even signal around amplitude axis results in the same signal. Examples of even signals are s[n] = \cos[2\pi f_0 n] and a quadratic signal s[n] = n^2 (see e.g., this Figure).

On the other hand, a signal is called odd (or anti-symmetric) if

    \begin{equation*}     s[-n] = -s[n] \end{equation*}

An odd signal has symmetry around the origin. Examples of an odd signal are s[n] = \sin[2\pi f_0 n] and s[n] = -n.

Periodic and Aperiodic

A signal is periodic if it repeats itself after a certain period N.

    \begin{equation*}     s[n\pm N] = s[n] \quad \textmd{for all} ~n \end{equation*}

Both s[n] = \cos[2\pi f_0 n] and s[n] = \sin[2\pi f_0 n] are examples of periodic signals if f_0 is a rational number.

If a signal does not repeat itself forever, there is no value of N that satisfies the above periodicity equation. Such a signal is known as aperiodic, an example of which is a unit step signal u[n] and most other signals encountered in this text.

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