Why is cos(n/6) aperiodic?

x(n) = cos(n6) is a non-periodic discrete signal because it doesn't satisfy the periodicity condition for discrete time signals i.e, it is not of the form 2π(mN).

1. How do you prove a signal is aperiodic?
2. Why is cos 2n not periodic?
3. Is a COS signal periodic?
4. What is meant by aperiodic signal?

How do you prove a signal is aperiodic?

Discrete Time Aperiodic Signal

If the condition of periodicity is not satisfied even for one value of n for a discrete time signal x(n), then the discrete time signal is aperiodic or nonperiodic.

Why is cos 2n not periodic?

x[n]=Cos(2n) is not periodic, as we need x [ n + N ] = x [ n ] ∀ n ∈ Z. where m ∈ Z.

Is a COS signal periodic?

If we look at the cosine function from x = 0 to x = 2π, we have an interval of the graph that's repeated over and over again in both directions, so we can see why the cosine function is a periodic function. This interval from x = 0 to x = 2π of the graph of f(x) = cos(x) is called the period of the function.

What is meant by aperiodic signal?

A signal that does not repeat itself after a specific interval of time is called an aperiodic signal. By applying a limiting process, the signal can be expressed as a continuous sum (or integral) of everlasting exponentials.