What is the periodicity of a discrete-time signal?

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). x(n) = cos(2π f n).

What are examples of discrete signals?

For example, if you were monitoring the temperature of a room, you would be able to take a measured value of temperature at any time. A discrete-time signal (sometimes referred to as a time-discrete signal or simply a discrete signal) is shown in Figure 15(b).

What are the types of representation of discrete-time signals illustrate with an example?

The weekly Dow Jones stock market index is an example of discrete-time signal. For example, the processing of speech on a digital computer requires the use of a discrete time sequence representing the values of the continuous-time speech signal at discrete points of time.

When is a discrete time signal a periodic signal?

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 are the periodicity of discrete time sinusoids?

Discrete-Time Sinusoids Discrete-Time Sinusoids: Frequency and Rate of Oscillation x[n] = Acos( n + ˚) Rate of oscillation increases as increasesUP TO A POINTthen decreases again and then increases again and then decreases again ….

What do you need to know about discrete frequency?

A very important issue to remember is that one needs to input exactly one or more periods, and that the FFT length must be that of a period or of multiples of a period. Notice that the MATLAB function sign is used to generate a periodic train of pulses from the cosine function.

How is the frequency domain represented in discrete time signals?

Section 2.6 develops the frequency domain representation of discrete-time sys- tems through the concept of complex exponentials as eigenfunctions, and Sections 2.7, 2.8, and 2.9 develop and explore the Fourier transform representation of discrete-time signals as a linear combination of complex exponentials.