Can anyone please tell me
What is the period of $\cos(n) u(n)$?
Here Cosine is multiplied by a unit step sequence . I am just learning the basics of signals now and I have found that $\cos(t) u(t)$ is aperiodic and no fundamental period in continuous domain, as Heaviside function is discontinuous at zero .what is the period in case of discrete where there is no jump in the sequence.
Let $\;f(n) := \cos(n)u(n)\;$ where $u(x)$ is the unit step function then $\;f(n) = 0\;$ for all $\;n<0.$ If $f(n)$ were periodic then it would be the zero sequence which it isn't. Thus, $f(n)$ is not periodic. In other words, the aperiodicity of $f$ comes from its zero values and not in its discontinuity.