Why are discrete-time signals periodic?

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). For this to be periodic, we must be able to find a non-zero integer p such that for all integers n, x(n + p) = cos(2π f n + 2π f p) = cos(2π f n) = x(n).

Is DFT periodic in frequency domain?

Taking these negative frequencies into account, the DFT views the frequency domain as periodic, with a period of 1.0 times the sampling rate, such as -0.5 to 0.5, or 0 to 1.0. Imagine a time domain signal that corresponds to some frequency spectrum.

Why is discrete time Fourier transform periodic?

The discrete-time Fourier transform (DTFT) gives us a way of representing frequency content of discrete-time signals. where T is a sufficiently small sampling step. Then X(Ω) can be thought of as a discretization of X(ω). Due to discrete-time nature of the original signal, the DTFT is 2π-periodic.

How a discrete-time signal can be represented in frequency domain?

Frequency Domain Representation of Discrete Time Signals & Systems. h[.] In other words a sinusoidal input to a discrete time LTI system provides a sinusoidal output. Discrete time Fourier Transform is a tool by which a time-domain sequence is mapped into a continuous function of a frequency variable.

How are discrete-time signals are classified?

Discrete time signals can be classified as follows: Periodic and non-periodic signals. Deterministic and random signals. Energy signals and power signals.

What discrete-time signals are?

A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal. This process is called sampling.

Which of the signal is discrete in time?

A digital signal is discrete in amplitude and time.