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Figure 1. A typical sum-of-products operation.
N-1 __\ z =(1/N) * / x(n) * y(n)-- n = 0

A sum-of-products operation

This notation means that a new value for z is calculated by multiplying the first N corresponding samples from each of two numeric series (x(n) and y(n)),calculating the sum of the products, and dividing the sum by N.

(In this module, I will be dealing primarily with numeric series that represent samples from a continuous function taken over time. Therefore, Iwill often refer to the numeric series as a time series.)

An alternative notation

The above notation requires about six lines of text to construct, and therefore could easily become scrambled during the HTML publishing process. Ihave invented an alternative notation that means exactly the same thing, but is less likely to be damaged during the publishing process. My new notation isshown in Figure 2 . You should be able to compare this notation with Figure 1 and correlate the terms in the notation to the verbal description of the operationgiven above.

Figure 2. Alternative notation for a sum-of-products operation.
z = (1/N) * S(n=0,N-1)[(x(n) * y(n)]

This is the notation that I will use in this module.

Preview

What is a time series?

I discussed the concept of a time series in some detail in my module titled Dsp00104-Sampled Time Series . For purposes of this module, suffice it to say that a time series is a set of sample values taken from a continuous function at equal increments of timeover a specified time interval. For example, if you were to record the temperature in your office every minute for six hours, the set of 360 differentvalues that you would record could be considered as a time series.

A new time series is produced

In DSP, we often multiply two time series together on a sample by sample basis. When I multiply the values in the time series x(n) by thecorresponding values in the time series y(n), that produces a new time series, which I will call w(n).

Calculation of the mean or average

If I compute the sum of the individual values in the series w(n), and then divide that sum by the number of samples, this is nothing more than thecalculation of the mean or average value of the time series named w(n). Most DSP operations boil down to nothing more complicated than calculating the averagevalue of the product of two time series.

Knowing what to multiply, when, and why

The real trick in DSP is knowing what to multiply, when to multiply it, and why to multiply it.

Some DSP algorithms are very complex. For example, the Fast Fourier Transform (FFT) algorithm, involves nothing more than a lot of multiply-add operations under the control of an extremely complex and efficient control structure.

In this module, I will concentrate on the Discrete Fourier Transform (DFT) algorithm, which is much less complex and therefore much easier to understand.

(While the DFT and the FFT produce the same results, the DFT typically runs much more slowly than the FFT, which is optimized for speed.)

Questions & Answers

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
Maciej
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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