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The module will introduce the concepts of a random signal and a random process.

Before now, you have probably dealt strictly with the theory behind signals and systems, as well as look at some the basiccharacteristics of signals and systems . In doing so you have developed an important foundation; however, most electrical engineers do notget to work in this type of fantasy world. In many cases the signals of interest are very complex due to the randomness ofthe world around them, which leaves them noisy and often corrupted. This often causes the information contained in thesignal to be hidden and distorted. For this reason, it is important to understand these random signals and how to recoverthe necessary information.

Signals: deterministic vs. stochastic

For this study of signals and systems, we will divide signals into two groups: those that have a fixed behavior and thosethat change randomly. As most of you have probably already dealt with the first type, we will focus on introducing you torandom signals. Also, note that we will be dealing strictly with discrete-time signals since they are the signals we dealwith in DSP and most real-world computations, but these same ideas apply to continuous-time signals.

Deterministic signals

Most introductions to signals and systems deal strictly with deterministic signals . Each value of these signals are fixed and can be determined by a mathematicalexpression, rule, or table. Because of this, future values of any deterministic signal can be calculated from pastvalues. For this reason, these signals are relatively easy to analyze as they do not change, and we can make accurateassumptions about their past and future behavior.

Deterministic signal

An example of a deterministic signal, the sine wave.

Stochastic signals

Unlike deterministic signals, stochastic signals , or random signals , are not so nice. Random signals cannot be characterized by a simple,well-defined mathematical equation and their future values cannot be predicted. Rather, we must use probability andstatistics to analyze their behavior. Also, because of their randomness, average values from a collection of signals are usually studied rather than analyzing one individual signal.

Random signal

We have taken the above sine wave and added random noise to it to come up with a noisy, or random, signal. Theseare the types of signals that we wish to learn how to deal with so that we can recover the original sine wave.

Random process

As mentioned above, in order to study random signals, we want to look at a collection of these signals rather than just oneinstance of that signal. This collection of signals is called a random process .

random process
A family or ensemble of signals that correspond to every possible outcome of a certain signal measurement. Eachsignal in this collection is referred to as a realization or sample function of the process.

Random sinusoidal process

A random sinusoidal process, with the amplitude and phase being random numbers.

A random process is usually denoted by X t or X n , with x t or x n used to represent an individual signal or waveform from this process.

In many notes and books, you might see the following notation and terms used to describe different types of randomprocesses. For a discrete random process , sometimes just called a random sequence , t represents time that has a finite number of values. If t can take on any value of time, we have a continuous random process . Often times discrete and continuous refer to the amplitude of the process, and process or sequencerefer to the nature of the time variable. For this study, we often just use random process to refer to a general collection of discrete-time signals, as seen above in .

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
Berger describes sociologists as concerned with
Mueller Reply
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Source:  OpenStax, Intro to digital signal processing. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10203/1.4
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