Signals & Systems - GATE practice papers - Electronics & Communication for Q. 526

Q.  Which among the below specified notations exhibit an odd signal? (Marks : 01)
- Published on 19 Oct 15

a. x(-t) = -x(t) & x[-n] = -x[n]
b. x(-t) = x(t) & x[-n] = x[n]
c. x(-t) = -x(-t) & x[-n] = -x[-n]
d. x(t) = x(-t) & x[n] = x[-n]

ANSWER: x(-t) = -x(t) & x[-n] = -x[n]
 
The necessary condition of an odd signal is that it must be zero at t=o or n=o . Thus, it can be expressed as x(-t) = -x(t) & x[-n] = -x[n].
This implies that negative value of time instants are equal to the negativity of an entire term in an odd signal, while the negative value of time instants are equal to the positive values of an entire term in an even signal.
However, sin t is an odd signal while cos t is an even signal

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