# Discrete time periodic signals

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This module contains information on discrete time periodic signals.

## Introduction

This module describes the type of signals acted on by the Discrete Time Fourier Series.

## Relevant spaces

The Discrete Time Fourier Series maps finite-length (or $N$ -periodic), discrete time signals in ${L}^{2}$ to finite-length, discrete-frequency signals in ${l}^{2}$ .

Periodic signals in discrete time repeats themselves in each cycle. However, only integers are allowed as time variable in discrete time. We denote signals in such case as x[n], n = ..., -2, -1, 0, 1, 2, ...

## Periodic signals

When a function repeats itself exactly after some given period, or cycle, we say it's periodic . A periodic function can be mathematically defined as:

$f(n)=f(n+mN)\forall m\colon m\in \mathbb{Z}$
where $N> 0$ represents the fundamental period of the signal, which is the smallest positive value of N for the signal to repeat. Because of this, you may also see a signal referred to as an N-periodic signal.Any function that satisfies this equation is said to be periodic with period N. Here's an example of a discrete-time periodic signal with period N:

We can think of periodic functions (with period $N$ ) two different ways:

1. as functions on all of $\mathbb{R}$
2. or, we can cut out all of the redundancy, and think of them as functions on an interval $\left[0 , N\right]()$ (or, more generally, $\left[a , a+N\right]()$ ). If we know the signal is N-periodic then all the information of the signal is captured by the above interval.

An aperiodic DT function $f(n)$ does not repeat for any $N\in \mathbb{R}$ ; i.e. there exists no $N$ such that this equation holds.

## Sindrilldiscrete demonstration

Here's an example demonstrating a periodic sinusoidal signal with various frequencies, amplitudes and phase delays:

## Conclusion

A discrete periodic signal is completely defined by its values in one period, such as the interval [0,N].

#### Questions & Answers

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Kyle
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what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Daniel
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there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Harper
Do you know which machine is used to that process?
s.
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for screen printed electrodes ?
SUYASH
What is lattice structure?
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Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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