Question

What is the even component of a discrete-time signal?

This question was addressed to me in examination.

I need to ask this question from Signal Classification and Properties topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

The even component of a discrete-time signal \( x[n] \) is the part of the signal that is symmetric around the origin. For any signal \( x[n] \), its even component \( x_e[n] \) can be calculated using:

\[

x_e[n] = \frac{x[n] + x[-n]}{2}

\]

In this expression:

- \( x[n] \) is the original signal.

- \( x[-n] \) is the time-reversed version of \( x[n] \).

The even component represents the part of the signal that does not change if the time index \( n \) is reversed. This is useful in analyzing the symmetry properties of signals in signal processing.