How do you know if a discrete signal is periodic?

How do you know if a discrete signal is 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). x(n) = cos(2π f n).

What are the various methods of representing discrete time signal?

There are three ways to represent discrete time signals. 2) Folding / Reflection : It is folding of signal about time origin n=0. In this case replace n by – n. 3) Addition : Given signals are x1(n) and x2(n), which produces output y(n) where y(n) = x1(n)+ x2(n).

How do you find the fundamental frequency of a discrete signal?

The smallest integer N for which this equation is satisfied is called the fundamental period. The frequency is then simply f = 1/N or 2*pi/N (in angular frequency, radians). So far there are not much difference besides the fact that N can only be a positive integer smaller than the signal length in the discrete case.

Are discrete-time sinusoids periodic?

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. The fundamental period is 31 which corresponds to k = 4 envelope cycles.

How do you know if a continuous time signal is periodic?

A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. In mathematical terms a signal x(t) is periodic if there is a number T such that for all t Equation 10.10 holds.

What are periodic signals?

A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. Examples of periodic signals include the sinusoidal signals and periodically repeated non-sinusoidal signals, such as the rectangular pulse sequences used in radar.

What are basic discrete-time signals?

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 one of the following is the discrete-time signal?

Explanation: A discrete-time signal is continuous in amplitude and discrete in time. It can either be present in nature or is sampled from an analog signal. A digital signal is discrete in amplitude and time.

What is the energy of a periodic signal?

Alternatively, the energy of a periodic signal with infinite extent, is infinite because it has finite power over each period and its extent is infinite. Consequently, periodic signals are power signals [4].

When is a discrete time signal a periodic 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 ). Note that, somewhat counterintuitively, not all sinusoidal discrete-time signals are periodic. Consider

Is the discrete time sinusoid periodic or non periodic?

Otherwise, the discrete-time sinusoid is non-periodic. Professor Deepa Kundur (University of Toronto)Discrete-Time Sinusoids6 / 23 Discrete-Time Sinusoids

Is the signal x ( t ) periodic or non periodic?

Recall if a signal x(t) is periodic, thenthere existsa T >0such that x(t) = x(t + T) If no T >0can be found, then x(t) is non-periodic. Professor Deepa Kundur (University of Toronto)Discrete-Time Sinusoids2 / 23 Discrete-Time Sinusoids

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.