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The real and imaginary parts of the spectrum

However, moving the impulse one sample into the future (a time delay) did change the values of the real and imaginary parts of the complex spectrum.As you can see from the third plot in Figure 7 , the real part of the spectrum is no longer a replica of the amplitude spectrum. Also the imaginary part of thespectrum in the fourth plot is no longer zero across the frequency range from zero to the folding frequency.

Real and imaginary values are intrinsically linked

However, the real and imaginary parts cannot change in arbitrary ways relative to one another. Recall that the amplitude spectrum at each individualfrequency is the square root of the sum of the squares of the real and imaginary parts. In order for the amplitude spectrum to stay the same, changes to the realpart of the spectrum must be accompanied by changes to the imaginary part that will maintain that relationship.

The phase angle spectrum

Finally, the phase angle shown in the bottom plot is no longer zero. Rather it is a straight line with a value of zero at zero frequency and a value of 180degrees at the folding frequency.

An important conclusion

Simply shifting an impulse forward or backward in time introduces a phase shift that is linear with frequency. Shifting the pulse forward in timeintroduces a linear phase shift with a positive slope. Shifting the pulse backwards in time introduces a linear phase shift with a negative slope. In bothcases, the amount of slope depends on the amount of time shift.

The converse is also true

A shift in time introduces a linear phase shift. Conversely, introducing a linear phase shift causes a shift in time.

A more acceptable form of phase distortion

Once again, consider your audio system. If your audio system introduces a phase shift across the frequency band of interest, you would probably like forthat phase shift to be linear with frequency. That will simply cause the music to be delayed in time. In other words, all frequency components in the musicwill be delayed an equal amount of time.

On the other hand, if the phase shift is not linear with frequency, some frequencies will delayed more than other frequencies. This sometimes results innoticeable phase distortion in your music.

Introduce a large time delay

Now let's move the impulse to the center of the eleven-sample pulse and observe the result. The new parameters are shown in Figure 8 .

Figure 8. Introduce a large time delay.
Parameters read from file Data length: 400Pulse length: 11 Sample for zero time: 0Lower frequency bound: 0.0 Upper frequency bound: 0.5Pulse Values 0.00.0 0.00.0 0.0180.0 0.00.0 0.00.0 0.0

The output from the spectral analysis

Figure 9 shows the result of performing a spectral analysis on the time series containing this new time-delayed impulse.

Figure 9. Spectral analysis of impulse with five-sample delay.
missing image

Finally, you can probably see the impulse on the left side of the top plot in Figure 9 without straining your eyes too much.

As we would expect, the amplitude spectrum hasn't changed.

Questions & Answers

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
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Akash Reply
it is a goid question and i want to know the answer as well
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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 ?
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.
what is the actual application of fullerenes nowadays?
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.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
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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.
Do you know which machine is used to that process?
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for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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Sravani Reply
what is system testing?
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
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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