# 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: A periodic discrete-time signal. Note how it repeats every 8 time units. 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.

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what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
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I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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..
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what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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Berger describes sociologists as concerned with
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