Question

Show whether the following signals are even, odd or neither. For the signals which are neither odd nor even, find and plot their even and odd components.

a. x[n] = u[n] - u[n-6] (plot the even and odd parts)
b. x[n] = n^2 cos(pi n/3)
c. x[n] = ne^-|n|

Answer 1

a) it is neither even nor odd

b) it is an even signal

c) it is an odd signal

Explanation:

A function f(x) or a signal is said to be even if its satisfies the condition of f(-x) = f(x). this implies that the graph of such a function or signal has a symmetrical relationship with respect to the y-axis.

A function f(x) or a signal is said to be odd if its satisfies the condition of f(-x) = - f(x). this implies that the graph of such a function or a signal has a skew-symmetrical relationship with respect to the y-axis.

from the first option ; a) x[n] = u[n] - u [n-6], from the conditions attached to even and odd functions, it can be inferred that the first option does not satisfy the conditions for even and odd functions hence, it is neither even nor odd.

The attachements below gives a detailed explanation of the second and third option.