The signal x(t) = e^(-5t) sin(t) is aperiodic.

Here's why:

A signal is said to be periodic if it repeats itself after a certain period of time, i.e., if there exists a T 0 such that x(t + T) = x(t) for all t.

In the given signal x(t) = e^(-5t) sin(t), the sin(t) part is periodic with a period of 2π. However, the e^(-5t) part is not periodic. It's an exponentially decaying function and does not repeat itself after any period of time.

Since both parts of the signal need to be periodic for the entire signal to be periodic, the signal x(t) = e^(-5t) sin(t) is aperiodic.

Question

The signal x(t) = e^(-5t) sin(t) is aperiodic.

Here's why:

A signal is said to be periodic if it repeats itself after a certain period of time, i.e., if there exists a T > 0 such that x(t + T) = x(t) for all t.

In the given signal x(t) = e^(-5t) sin(t), the sin(t) part is periodic with a period of 2π. However, the e^(-5t) part is not periodic. It's an exponentially decaying function and does not repeat itself after any period of time.

Since both parts of the signal need to be periodic for the entire signal to be periodic, the signal x(t) = e^(-5t) sin(t) is aperiodic.

Knowee AI · Accepted Answer

The signal x(t) = e^(-5t) sin(t) is aperiodic.

Here's why:

A signal is said to be periodic if it repeats itself after a certain period of time, i.e., if there exists a T > 0 such that x(t + T) = x(t) for all t.

In the given signal x(t) = e^(-5t) sin(t), the sin(t) part is periodic with a period of 2π. However, the e^(-5t) part is not periodic. It's an exponentially decaying function and does not repeat itself after any period of time.

Since both parts of the signal need to be periodic for the entire signal to be periodic, the signal x(t) = e^(-5t) sin(t) is aperiodic.

he signal x(t) = e^(-5t) sin(t) is1 pointPeriodic and aperiodic bothNothing can be said.periodicaperiodic

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