# 1.2 Signal properties

## Signal classification

Signals can be broadly classified as discrete-time or continuous-time, depending on whether the independent variable is integer-valued or real-valued. Signals may also be either real-valued or complex-valued. We will now consider some of the other ways we can classify signals.

## Signal length: finite/infinite

This classification is just as it sounds. An infinite-length discrete-time signal takes values for all time indices: all integer values $n$ on the number line from $-$ all the way up to  . A finite-length signal is defined only for a certain range of $n$ , from some ${N}_{1}$ to ${N}_{2}$ . The signal is not defined outside of that range.

## Signal periodicity

As the name suggests, periodic signals are those that repeat themselves. Mathematically, this means that there exists some integer value $N$ for which $x(n+N)=x(n)$ , for all values of $n$ . So if we define a fundamental period of this particular signal of length, like $N=8$ , then we will see the same signal values shifted by $8$ time indices, by $16$ , $-8$ , $-16$ , etc. Below is an example of a periodic signal: So periodic signals repeat, and clearly periodic signals are going to be, therefore, infinite in length.It's also important to remember that to be periodic in discrete-time, the period $N$ must be an integer. If there is no such integer-valued $N$ for which $x(n+N)=x(n)$ (for all values of $n$ ), then we classify the signal as being aperiodic .

## Converting between infinite and finite length

In different applications, the need will arise to convert a signal from infinite-length to finite-length, and vice versa. There are many ways this operation can be accomplished, but we will consider the most common.

The most straightforward way to create a finite-length signal from an infinite-length one is through the process of windowing . A windowing operation extracts a contiguous portion of an infinite-length signal, that portion becoming the new finite-length signal. Sometimes a window will also scale the smaller portion in a particular way. Below is a mathematical expression of windowing (without any scaling):

$y(n)=\begin{cases}x(n) & \text{if {N}_{1}\le n\le {N}_{2}}\\ \text{undefined} & \text{if \text{else}}\end{cases}$

Below is a signal $x(n)$ (assume it is infinite-length, with only a part of it shown), with a portion of it extracted to create $y(n)$ :

There are two ways a signal can be converted from a finite-length to infinite-length. The first is referred to as zero-padding . It is easy to take a finite-length signal and then make a larger finite-length signal out of it: just extend the time axis. We have to decide what values to put in the new time locations, and simply putting $0$ at all the new locations is a common approach. Here is how it looks, mathematically, to create a longer signal $y(n)$ from a shorter signal $x(n)$ defined only on ${N}_{1}\le n\le {N}_{2}$ :

$y(n)=\begin{cases}0 & \text{if {N}_{0}\le n< {N}_{1}}\\ x(n) & \text{if {N}_{1}\le n\le {N}_{2}}\\ 0 & \text{if {N}_{2}< n\le {N}_{3}}\end{cases}$

Here, obviously ${N}_{0}< {N}_{1}< {N}_{2}< {N}_{3}$ , and if we extend ${N}_{0}$ and ${N}_{3}$ to negative and positive infinity, respectively, then $y(n)$ will end up being infinite-length.

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
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
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
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