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(The curve in Figure 4 can also be considered to consist of the sum of two parts. However, in Figure 4 , the bias value is zero.)

The net area

The net area contributed by the periodic part of the curve in Figure 5 continues to be zero. In effect, the non-zero net area under the curve in Figure 5 is the amount of the positive bias multiplied by the number of points. In other words, because I captured an even number of cycles of the periodic portionof the curve in my calculation of net area, only the bias contributes a non-zero value to the net area under the total curve.

Part of a cycle

Had I failed to capture an even number of cycles of the periodic portion of the curve, then the positive lobes might not completely cancel the negativelobes, and the net area under the curve would be influenced by the periodic portion of the curve in addition to the bias.

Why is this important?

These concepts are extremely important in this module as we learn how to do frequency spectral analysis.

As you will see in this module, in doing frequency spectral analysis, we will form a product between a target time series and a sinusoid. The purpose is tomeasure the power contained in the time series at the frequency of the sinusoid.

The product of the target time series and the sinusoid will produce the sum of a potentially infinite number of periodic functions, some of which may beriding on a positive or negative bias. We will measure the amount of bias by computing the average value of the product time series. The amount of bias willbe our estimate of the power contained in the target time series at the frequency of the sinusoid.

The Fourier transform

There is a mathematical process, known as the Fourier transform, which can be used to linearly transform information back and forth between two differentdomains. The information can be represented by sets of complex numbers in either or both domains.

The domains can represent a variety of different things. In DSP, the domains are often referred to as the time domain and the frequency domain , but that is not a requirement. For example, one of the domains could representthe samples that make up the pixels in a photograph and the other domain could represent something having to do with the manipulation of photographs.

Usually when dealing with the time domain and the frequency domain, the values that make up the samples in the time domain are purely real while thevalues that make up the samples in the frequency domain are complex containing both real and imaginary parts.

Time domain and frequency domain

For some purposes, it is preferable to have your information in the time domain. For other purposes, it is preferable to have your information in thefrequency domain. The Fourier transform allows you to transform your information back and forth between these two domains at will.

For example, it is possible to transform information from the time domain into the frequency domain, modify that information in the frequency domain, andthen transform the modified information back into the time domain. This is one way to accomplish frequency filtering.

Questions & Answers

what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
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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