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Spectrum of an ideal sinusoid

That having been said, different people will probably interpret these results in different ways. Let's begin by stating that the theoretical spectrum for asinusoid of infinite length in the absence of noise is a single vertical line having zero width and infinite height.

In the real world of measurements, however, there is no such thing as a sinusoid of infinite length. Rather, every measurement that we make musttruncate the sinusoid at some point in time. For a theoretical signal of infinite length, every spectral analysis that we can perform is an imperfectestimate of the spectrum.

Two viewpoints

There are at least two ways to think of the pulses shown in Figure 1 .

  1. Each pulse is a truncated section of an ideal sinusoid of infinite length.
  2. Each pulse is a signal having a definite planned start and stop time.

The way that you interpret the results shown in Figure 2 depends on your viewpoint regarding the pulses.

The first viewpoint

If your viewpoint is that each pulse is a truncated section of an ideal sinusoid of infinite length, then the width of each of the peaks (beyond zero width) is the result of measurement error introduced by the truncation process.

The second viewpoint

If your viewpoint is that each pulse is a signal having a definite planned start and stop time, then the widths and the shape of each of the peaksdescribes the full range of frequency components required to physically generate such a pulse. This is the viewpoint that is consistent with the hypothetical situation involving a device on a submarine that I described earlier in this module.

A simplified hypothetical situation

Assume for the moment that the hypothetical device on the submarine contains only one rotating machine and that this device is turned on and off occasionallyin short bursts. Because of the rotating machine, when the device is turned on, it will emit acoustic energy whose frequency matches the rotating speed of themachine.

(In reality, it will probably also emit acoustic energy at other frequencies as well, but we will consider it to be a very ideal machine. Wewill also assume the complete absence of any other acoustic noise in the environment.)

Assume that you have a recording window of 400 samples, and that you are able to record five such bursts within each of five separate recording windows.Further assume that the lengths of the individual bursts match the time periods indicated by the pulses in Figure 1 .

The spectra of the bursts

If you perform spectral analysis on each of the five individual 400-sample windows containing the bursts, and if you normalize the peak values for plottingpurposes, you should get results similar to those shown in Figure 2 .

The spectral bandwidth of the signal

The frequency range over which energy is distributed is referred to as the bandwidth of the signal. As you can see in Figure 2 , shorter pulses require wider bandwidth.

For example, considerably more bandwidth is required of a communication system that is required to reliably transmit a series of short truncatedsinusoids than one that is only required to reliably transmit a continuous tone at a single frequency.

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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