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As you can see from Listing 6 , the values that make up the pulse are produced by adding together the values of two different cosine functions having differentfrequencies. The values for freq1 and freq2 are as described above.

You can view the remainder of this program in Listing 11 .

Spectral analysis output

The results of running the program named Dsp032 and displaying the results with the program named Graph03 are shown in Figure 5 .

Figure 5. Spectral analyses of five pulses.
missing image

Each of the peaks in the third, fourth, and fifth plots in Figure 5 corresponds to the frequency of one of the two sinusoids that were addedtogether to produce the pulses shown in Figure 4 .

Can we answer the original question now?

The question posed in the original hypothetical situation was "how long must the operating bursts of this device be in order for you to resolve the peaks and identify the enemy submarine under ideal conditions?"

We are looking at very ideal conditions in Figure 4 and Figure 5 . In particular, the pulses exist completely in the absence of noise.

(The existence of wide-band noise added to the pulses in Figure 4 would cause a change in the spectral results in Figure 5 . That change might be described as having the appearance of grass and weeds growing on thebaseline across the entire spectrum. The stronger the wide-band noise, the taller would be the weeds.)

Cannot resolve two peaks for first two pulses

Clearly for the ideal condition of recording the bursts in the total absence of noise, you cannot resolve the peaks from the top two plots in Figure 5 . For those two pulses, the spectral peaks simply merge together to form a singlebroad peak. Therefore, for this amount of separation between the frequencies of the two sinusoids, the lengths of the first two pulses in Figure 4 are insufficient to allow for separation and identification of the separate peaks.

We must be in luck

We seem to have the problem bracketed. (Were we really lucky, or did I plan it this way?) Under the ideal conditions of this experiment, the peaks are separable in the middle plot of Figure 5 . Thus, for the amount of separation between the frequencies of the two sinusoids, the length of the third pulse is Figure 4 is sufficient to allow for separation and identification of the separate peaks.

A qualified answer to the question

The peaks are even better separated in the bottom two plots in Figure 5 . For the five pulses used in this experiment and the amount of separation between thefrequencies of the two sinusoids, any pulse as long or longer than the length of the third pulse is Figure 4 is sufficient to allow for separation and identification of the separate peaks.

What about the effects of noise?

If you were to add a nominal amount of wide-band noise to the mix, it would become more difficult to resolve the peaks for the bottom three plots in Figure 5 because the peaks would be growing out of a bed of weeds.

(If you add enough wide-band noise, you couldn't resolve the peaks using any of the plots, because the peaks would be completely "lost in thenoise.")

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
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Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
what's the program
Jordan
?
Jordan
what chemical
Jordan
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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