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Although it wasn't apparent in Figure 7 , Figure 9 shows that the real part of the spectrum takes on the shape of a cosine wave, while the imaginary part ofthe spectrum takes on the shape of a sine wave as a result of the time delay of the impulse.

The phase shift is still linear across frequency as would be expected, but the slope is now five times greater than the slope of the phase shift in Figure 7 .

(Note that the time delay is five times greater in Figure 9 . Note also that the plot of the phase angle wraps around from +180 degrees to -180degrees each time the phase angle reaches +180 degrees. This produces the saw tooth effect shown in the bottom plot in Figure 9 .)

A boxcar pulse

If an impulse is the simplest kind of pulse to generate digitally, a boxcar pulse is probably the next simplest. A "boxcar" pulse is one where severaladjacent samples have the same non-zero value. Let's examine the case for an eleven-sample boxcar pulse. The new parameters for this case are shown in Figure 10 .

Figure 10. A boxcar pulse.
Parameters read from file Data length: 400Pulse length: 11 Sample for zero time: 0Lower frequency bound: 0.0 Upper frequency bound: 0.5Pulse Values 40.040.0 40.040.0 40.040.0 40.040.0 40.040.0 40.0

The spectral analysis output for the boxcar pulse

The spectral analysis output for the eleven-sample boxcar pulse is shown in Figure 11 .

Figure 11. Spectral analysis of 11-sample boxcar pulse.
missing image

The pulse itself is relatively easy to see on the leftmost end of the top plot.

The amplitude spectrum

The amplitude spectrum is no longer flat. Rather it has a peak at zero frequency and goes to zero between frequency sample 72 and frequency sample 73.

Without getting into the technical details, I will simply tell you that the location of the point where it goes to zero is related to the reciprocal of thepulse width. If that sounds familiar, it is because we encountered similar situations involving bandwidth in the module titled Spectrum Analysis using Java, Frequency Resolution versus Data Length .

In fact, the shape of the amplitude spectrum is a familiar (sin x)/x curve with the negative lobes flipped up and turned into positive lobes instead.

The phase angle is still linear with frequency although it now shows some discontinuities at those frequencies where the amplitude spectrum touches zero.

The magic of non real-time digital processing

When working with (recorded non real-time) digital time series, it is not only possible to physically shift pulses forward or backward in time, itis also possible to leave the pulses where they are and redefine the underlying time base. For the next experiment, I will leave everything else the same andredefine the location of the origin of time. I will place the time origin at themiddle of the boxcar pulse.

The new parameters for this experiment are shown in Figure 12 . Note that the only significant difference between Figure 12 and Figure 10 is the redefinition of the sample that represents zero time. I redefined the time origin from sample0 to sample 5. This causes the boxcar pulse to be centered on zero time. Five of the samples in the boxcar pulse occur in negative (history) time. One sample occurs exactly at zero time. The other five samples occur in positive (future) time .

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
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
how can I make nanorobot?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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