# 1.4 Common discrete time signals

 Page 1 / 1
Presents several useful discrete time signals.

## Introduction

Before looking at this module, hopefully you have an idea of what a signal is and what basic classifications and properties a signal canhave. In review, a signal is a function defined with respect to an independent variable. This variable is often timebut could represent any number of things. Mathematically, discrete time analogsignals have discrete independent variables and continuous dependent variables. This module will describe some useful discrete time analog signals.

## Sinusoids

One of the most important elemental signal that you will deal with is the real-valued sinusoid. In its discrete-timeform, we write the general expression as

$A\cos (\omega n+\phi )$
where $A$ is the amplitude, $\omega$ is the frequency, and $\phi$ is the phase. Because n only takes integer values, the resulting function is only periodic if $\frac{2\pi }{\omega }$ is a rational number. Note that the equation representation for a discrete time sinusoid waveform is not unique.

## Complex exponentials

As important as the general sinusoid, the complex exponential function will become a critical part of your study of signals and systems. Its general discrete form iswritten as

$z^{n}$
where $z$ , is a complex number. The set of complex exponentials for which $\left|z\right|=1$ are a special class, expressed as $e^{j\omega n}$ , (where $\omega$ is the angular position on the unit circle, in radians).

The discrete time complex exponentials have the following property.

$e^{j\omega n}=e^{j(\omega +2\pi )n}$
Given this property, if we have a complex exponential with frequency $\omega +2\pi$ , then this signal "aliases" to a complex exponential with frequency $\omega$ , implying that the equation representations of discrete complex exponentials are not unique.

## Unit impulses

The second-most important discrete-time signal is the unit sample , which is defined as

$\delta (n)=\begin{cases}1 & \text{if n=0}\\ 0 & \text{otherwise}\end{cases}$

More detail is provided in the section on the discrete time impulse function. For now, it suffices to say that this signal is crucially important in the study of discrete signals, as it allows the sifting property to be used in signal representation and signal decomposition.

## Unit step

Another very basic signal is the unit-step function defined as

$u(n)=\begin{cases}0 & \text{if n< 0}\\ 1 & \text{if n\ge 0}\end{cases}$

The step function is a useful tool for testing and for defining other signals. For example, whendifferent shifted versions of the step function are multiplied by other signals, one can select a certain portion of thesignal and zero out the rest.

## Common discrete time signals summary

Some of the most important and most frequently encountered signals have been discussed in this module. There are, of course, many other signals of significant consequence not discussed here. As you will see later, many of the other more complicated signals will be studied in terms of those listed here. Especially take note of the complex exponentials and unit impulse functions, which will be the key focus of several topics included in this course.

Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
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
what is the Synthesis, properties,and applications of carbon nano chemistry
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?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!