The signal x(t) = e^(-4t) cos(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 positive constant T such that x(t) = x(t+T) for all t.

In the given signal x(t) = e^(-4t) cos(t), the cosine function cos(t) is periodic with a period of 2π. However, the exponential function e^(-4t) is not periodic as it does not repeat itself after a certain period of time.

Since the product of a periodic function and an aperiodic function is aperiodic, the given signal x(t) = e^(-4t) cos(t) is aperiodic.

Question

The signal x(t) = e^(-4t) cos(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 positive constant T such that x(t) = x(t+T) for all t.

In the given signal x(t) = e^(-4t) cos(t), the cosine function cos(t) is periodic with a period of 2π. However, the exponential function e^(-4t) is not periodic as it does not repeat itself after a certain period of time.

Since the product of a periodic function and an aperiodic function is aperiodic, the given signal x(t) = e^(-4t) cos(t) is aperiodic.

Knowee AI · Accepted Answer

The signal x(t) = e^(-4t) cos(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 positive constant T such that x(t) = x(t+T) for all t.

In the given signal x(t) = e^(-4t) cos(t), the cosine function cos(t) is periodic with a period of 2π. However, the exponential function e^(-4t) is not periodic as it does not repeat itself after a certain period of time.

Since the product of a periodic function and an aperiodic function is aperiodic, the given signal x(t) = e^(-4t) cos(t) is aperiodic.

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