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Create more complex experiments. For example, you could create pulses containing three or more sinusoids at closely spaced frequencies, and you couldcause the amplitudes of the sinusoids to be different. See what it takes to cause the peaks in the spectra of those pulses to be separable and identifiable.

If you really want to get fancy, you could create a pulse consisting of a sinusoid whose frequency changes with time from the beginning to the end of thepulse. (A pulse of this type is often referred to as a frequency modulated sweep signal.) See what you can conclude from doing spectral analysis on a pulse of this type.

Try using the random number generator of the Math class to add some random noise to every value in the 400-sample time series. See whatthis does to your spectral analysis results.

Move the center frequency up and down the frequency axis. See if you can explain what happens as the center frequency approaches zero and as the centerfrequency approaches the folding frequency.

Most of all, enjoy yourself and learn something in the process.


This program provides the code for three spectral analysis experiments of increasing complexity.

Bandwidth versus pulse length

The first experiment performs spectral analyses on five simple pulses consisting of truncated sinusoids. This experiment shows:

  • Shorter pulses require greater bandwidth.
  • The bandwidth of a truncated sinusoidal pulse is inversely proportional to the length of the pulse.

Peak resolution versus pulse length and frequency separation

The second experiment performs spectral analyses on five more complex pulses consisting of the sum of two truncated sinusoids having closely spacedfrequencies. The purpose is to determine the required length of the pulse in order to use spectral analysis to resolve spectral peaks attributable to the twosinusoids. The experiment shows that the peaks are barely resolvable when the length of the pulse is the reciprocal of the frequency separation between thetwo sinusoids.

Five pulses with barely resolvable spectral peaks

The third experiment also performs spectral analyses on five pulses consisting of the sum of two truncated sinusoids having closely spacedfrequencies. In this case, the frequency separation for each pulse is the reciprocal of the length of the pulse. The results of the spectral analysisreinforce the conclusions drawn in the second experiment.

What's next?

So far, the modules in this series have ignored the complex nature of the results of spectral analysis. The complex results have been converted into realresults by computing the square root of the sum of the squares of the real and imaginary parts.

The next module in the series will meet the issue of complex spectral results head on and will explain the concept of phase angle. In addition, the modulewill explain the behavior of the phase angle with respect to time shifts in the input time series.

Complete program listings

Complete listings of the main programs discussed in this module are provided in this section. Listings for other programs mentioned in the module, such as Graph03 and Graph06 , are provided in other modules. Those modules are identified in the text of this module.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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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