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Where is that impulse?

If you strain your eyes and you know exactly where to look, you may be able to see a single black spike with an amplitude of 180 at the far left of the topplot. If you can't see it, you will simply have to trust me when I tell you that it is there.

The amplitude spectrum

Now take a look at the amplitude spectrum in the second plot from the top. What you should see is a straight black line extending from zero to the foldingfrequency on the right. This is because such an impulse (theoretically) contains an equal distribution of energy at every frequency from zero toinfinity.

(In reality, there is no such thing as a perfect impulse, so there is no such thing as infinite bandwidth. However, the bandwidth of a practicalimpulse is very wide and the amplitude spectrum is very flat.)

That is one of the things that make the impulse so useful. It is often used for various testing purposes in both the analog world and the digital world.

The real spectrum

Now look at the real spectrum in the second plot from the top. As you can see, it looks exactly like the amplitude spectrum. This is because the impulseappears at zero time. We will change this in the next experiment so that you can see the impact of a time delay on the complex spectrum.

The imaginary spectrum

Moving on down the page, the imaginary part of the spectrum is a flat line with a value of zero across the entire frequency range. Once again, this isbecause the impulse appears at zero time.

The phase angle

Because the imaginary value is zero everywhere, the ratio of the imaginary value to the real value is also zero everywhere. Thus, the phase angle is alsozero at all frequencies within the range.

Introduce a time delay

Now we are going to introduce a one-sample time delay in the location of the impulse relative to the time origin. We will keep the zero time reference at thefirst sample and cause the impulse to appear as the second sample in the eleven-sample sequence.

The new parameters are shown in Figure 6 . The only change is the move of the impulse from the first sample in the eleven-sample pulse to the second sample inthe eleven-sample pulse.

Figure 6. Introduce a 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 0.0180.0 0.00.0 0.00.0 0.00.0 0.00.0 0.0

The spectral analysis output

The result of performing the spectral analysis on this new time series is shown in Figure 7 .

Figure 7. Spectral analysis of an impulse with a one-sample delay.
missing image

Once again, if you strain your eyes, you may be able to see the impulse on the left end of the top plot. It has been shifted one sample to the rightrelative to that shown in Figure 5 .

The amplitude spectrum

The amplitude spectrum in the second plot looks exactly like it looked in Figure 5 . That is as it should be. The spectral content of a pulse is determined by its waveform, not by its location in time. Simply moving the impulse by onesample into the future doesn't change its spectral content.

Questions & Answers

How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
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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