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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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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