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What can we learn from this?

Since we have concluded that the middle pulse in Figure 4 is sufficiently long to allow us to resolve the two peaks, let's see what we can learn from theparameters that describe that pulse.

Pulse length and frequency separation

To begin with, the length of the pulse is 100 samples.

What about the frequency separation of the two sinusoids? Recall that the frequency of one sinusoid is (0.0625 - 2.0/len) times the sampling frequency,where len is the length of the time series containing the pulse. The frequency of the other sinusoid is (0.0625 + 2.0/len) times the sampling frequency.

Thus, total separation between the two frequencies is 4/len, or 4/400. Dividing through by 4 we see that the separation between the two frequencies is1/100.

Eureka, we have found it

For the third pulse, the frequency separation is the reciprocal of the length of the pulse . Also, the length of the third pulse is barely sufficient to allow for separation and identification of the two peaks in the spectrum.

Thus, the two spectral peaks are separable in the absence of noise if the frequencyseparation is the reciprocal of the pulse length. (That is too good to be a coincidence. I must have planned that way.)

Thus, we have reached another conclusion. Under ideal conditions, the two peaks in the spectrum can be resolved when the separation between the frequencies of the two sinusoids is equal tothe reciprocal of the pulse length.

The general answer

There is no single answer to the question "how long must the operating bursts of this device be in order for you to resolve the peaks andidentify the enemy submarine under ideal conditions?"

The answer depends on the frequency separation. The general answer is that the length of the bursts must be at least as long as the reciprocal of thefrequency separation for the two sinusoids. If the separation is large, the pulse length may be short. If the separation is small, the pulse length must belong.

The program named Dsp032

As I indicated earlier, the plots shown in Figure 5 were the result of running the program named Dsp032 and displaying the data with the program named Graph03 .

The only thing that is new in this program is the code that generates the five pulses and saves them in their respective data arrays. Even that code isnot really new, because it is identical to the code shown in Listing 6 . Therefore, I won't discuss this program further in this module.

One more experiment

As you can surmise from the conclusions reached above, in order to be able to resolve the two peaks in the spectrum, you can either keep the pulse length thesame and increase the frequency separation, or you can keep the frequency separation the same and increase the pulse length.

Let's examine an example where we keep the pulse lengths the same as before and adjust the frequency separation between the two sinusoids to make it barelypossible to resolve the peaks for each of the five pulses.

We will need to increase the frequency separation for the first two pulses, and we can decrease the frequency separation for the fourth and fifth pulses. Wewill leave the frequency separation the same as before for the third pulse since it already seems to have the optimum relationship between pulse length andfrequency separation.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
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.
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
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
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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