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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

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
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Damian Reply
absolutely yes
Daniel
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Akash Reply
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Maciej
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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
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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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
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
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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
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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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