Discrete-time signals increase in frequency and period

1. How does increasing the frequency of a signal change the period of a signal?
2. What is the period of the discrete-time signal?
3. Are all discrete-time signals periodic?
4. What is frequency response of discrete-time signal?

How does increasing the frequency of a signal change the period of a signal?

The frequency of the signal tells how many periods of the signal occur within one second—the higher the frequency, the more rapidly the signal is changing. Time varying signals are generally categorized by overall shape, frequency, amplitude, and offset.

What is the period of the discrete-time signal?

Therefore, a discrete-time sinusoid is periodic if its radian frequency Ω is a rational multiple of π. Otherwise, the discrete-time sinusoid is non-periodic. The fundamental period is 12 which corresponds to k = 1 envelope cycles.

Are all discrete-time signals periodic?

Such signals are called discrete-time signals. A discrete-time signal is periodic if there is a non-zero integer p ∈ DiscreteTime such that for all n ∈ DiscreteTime, x(n + p) = x(n).

What is frequency response of discrete-time signal?

A discrete-time signal of fundamental period N can consist of frequency components separated by 2π/N radians or f = 1/N cycles. Consequently, the Fourier series representation of the discrete-time periodic signal will contain at most N frequency components. This is the basic difference between the Fourier series.