Sinusoidal signal

All continuous-time signals are periodic. The discrete-time sinusoidal sequences may or may not be periodic. They depend on the value of ω. For a discrete time signal to be periodic, the angular frequency ω must be a rational multiple of 2π.

A discrete sinusoidal signal is shown in the figure above.

Discrete form of a sinusoidal signal can be represented in the format −

x(n)=Asin(ωn+ϕ)$$x(n)=A\sin (\omega n+\varphi )$$

Here A,ω and φ have their usual meaning and n is the integer. Time period of the discrete sinusoidal signal is given by −

N=2πmω$$N=\frac{2\pi m}{\omega }$$

Where, N and m are integers.