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Figure 12. Shift the time base.
Parameters read from file Data length: 400Pulse length: 11 Sample for zero time: 5Lower frequency bound: 0.0 Upper frequency bound: 0.5Pulse Values 40.040.0 40.040.0 40.00140.0 40.040.0 40.040.0 40.0

(I did make one other change. This change was to add a tiny spike to one of the samples near the center of the pulse. This creates a tiny amountof wide-band energy and tends to stabilize the computation of the phase angle. It prevents the imaginary part of the spectrum from switching backand forth between very small positive and negative values due to arithmetic errors.)

The spectral analysis output

The output from the spectral analysis is shown in Figure 13 . The magnitude spectrum hasn't changed. The real part of the spectrum has changedsignificantly. It is now a true (sin x)/x curve with both positive and negative lobes.

Figure 13. Spectral analysis of 11-sample boxcar centered in time.
missing image

The imaginary part of the spectrum is zero or nearly zero at every frequency. (It would be zero in the absence of arithmetic errors.)

The phase angle is zero across the entire main energy lobe of the spectrum. It is -180 degrees in those frequency areas where the real part of the spectrumis negative, and is zero in those frequency areas where the real part of the spectrum is positive. There is no linear phase shift because the boxcar pulse iscentered on the time origin.

Probably more than you ever wanted to know

And that is probably more than you ever wanted to know about the complex spectrum, phase angles, and time shifts. I will stop writing and leave it atthat.

Run the program

I encourage you to copy, compile, and run the program provided in this module. Experiment with it, making changes and observing the results of yourchanges.

Create more complex experiments. For example, you could create pulses of different lengths with complex shapes and examine the complex spectra and phaseangles for those pulses.

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. Pay particular attention to the phase angle across thefrequency band containing most of the energy.

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


The default pulse for the Dsp034 program is a damped sinusoid. This is a pulse whose shape is commonly found in mechanical andelectronic systems in the real world. The phase angle in the complex spectrum for a pulse of this shape is nonlinear. Among other things, nonlinear phaseangles introduce phase distortion into audio systems.

The simplest pulse of all is a single impulse. A pulse of this type has an infinite bandwidth (theoretically) and a linear phase angle. The slope of the phase angle depends on the location of the pulse relative to the timeorigin.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
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kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
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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.
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Commplementary angles
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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+_
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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
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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
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Damian Reply
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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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
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how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
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I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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
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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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