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The real part of the spectrum is symmetrical

The real part of the complex spectrum is shown in the second plot from the top in Figure 1 . It will become important later to note that the real part of the spectrum is symmetrical about the folding frequency near the center of theplot (at the eighth tick mark) .

Without attempting to explain why, I will simply tell you that the real part of the Fourier transform of a complex series whose imaginary part is all zeros (like a typical sampled time series for real-world data) is always symmetrical about the folding frequency.

The imaginary part of the spectrum is asymmetrical

The imaginary part of the complex spectrum is shown in the third plot from the top. Again, it will become important later to note that the imaginary partof the spectrum is asymmetrical about the folding frequency.

Once again, without attempting to explain why, the imaginary part of the Fourier transform of a complex series whose imaginary part is all zeros (like a typical sampled time series for real-world data) is always asymmetrical about the folding frequency.

The converse is also true

It is also true that the values of the imaginary part of the Fourier transform of a complex spectrum whose real part is symmetrical about the foldingfrequency and whose imaginary part is asymmetrical about the folding frequency will all be zero. I will take advantage of these facts later to simplify thecomputing and plotting process.

The amplitude spectrum

The amplitude spectrum is shown in the fourth plot down from the top. Recall from previous modules that the amplitude values are always positive, consistingof the square root of the sum of the squares of the real and imaginary parts.

The output time series

The output time series, produced by performing an inverse Fourier transform on the complex spectrum is shown in the bottom plot in Figure 1 . Compare the bottom plot to the top plot. As you can see, they are the same, demonstratingthe reversible nature of the Fourier transform.

The program named Dsp035

I will discuss this program in fragments. A complete listing of the program is provided in Listing 14 near the end of the module.

The beginning of the class named Dsp035

The beginning of the class for Dsp035 , including the declaration of some variables and the creation of some array objects is shown in Listing 1 . This code is straightforward.

Listing 1. The beginning of the class named Dsp035.
class Dsp035 implements GraphIntfc01{ final double pi = Math.PI;int len = 256; double[]timeDataIn = new double[len];double[] realSpect = new double[len]; double[]imagSpect = new double[len];double[] angle = new double[len];//unused double[]magnitude = new double[len];double[] timeDataOut = new double[len];

Beginning of the constructor

The constructor begins in Listing 2 . The code in Listing 2 creates the input time series data shown in the top plot of Figure 1 .

Listing 2. Beginning of the constructor.
public Dsp035(){//constructor //Create the raw data pulsestimeDataIn[0] = 0;timeDataIn[1] = 50;//... //code deleted for brevity//... timeDataIn[254]= -80; timeDataIn[255]= -80; //Create raw data sinusoidfor(int x = len/3;x<3*len/4;x++){ timeDataIn[x]= 80.0 * Math.sin( 2*pi*(x)*1.0/20.0);}//end for loop

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
salma
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
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
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?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
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
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
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
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
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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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