# Java1478-fun with java, how and why spectral analysis works  (Page 2/9)

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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.

## 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.)

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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
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
how nano science is used for hydrophobicity
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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