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( Figure 4 shows the values read from the file named Dsp029.txt and displayed in an improved format.)

In this case, the third frequency in the list is one-half the sampling frequency, which is the folding frequency. The two frequencies on either side ofthat one have values that are symmetrical about the folding frequency.

Figure 4. A new set of frequency values.
Data length: 50 Number sinusoids: 5Frequencies 0.1250.25 0.50.75 0.875Amplitudes 90.090.0 90.090.0 90.0

The program output

The five horizontal plots in Figure 5 show the result of running the program named Dsp029 with the frequencies shown in Figure 4 .

Figure 5. Program output for five sinusoids.
missing image

The center plot in Figure 5 is the sampled representation of the folding frequency.

The top two plots in Figure 5 are obviously the sampled representations of the two lower frequencies specified by the first two frequencies in Figure 4 .

Not so obvious ...

However, it is not so obvious that the bottom two plots in Figure 5 are the sampled representations of the two higher frequencies specified by the last twofrequencies in Figure 4 . They look exactly like the top two plots but in reverse order.

Unable to distinguish ...

Frequencies above one-half the sampling frequency are not distinguishable by viewing the sampled data. In fact, they are converted to lower frequencies bysampling process. The new lower frequencies fold around a point in the frequency spectrum given by one-half the sampling frequency. That is why it is called thefolding frequency. (In 1933, this frequency was named after scientist Harry Nyquist .)

One more example

Let's look at one more example of plotted sinusoids. Consider the frequency values shown in Figure 6 . The second and third frequencies are symmetrical about the sampling frequency. The fourth and fifth frequencies are symmetrical abouttwice the sampling frequency. The first frequency value is the same distance from zero as the other four frequencies are from the sampling frequency andtwice the sampling frequency.

Figure 6. One more example.
Data length: 50 Number sinusoids: 5Frequencies 0.10.9 1.11.9 2.1Amplitudes 90.090.0 90.090.0 90.0

The program output

Figure 7 shows the output produced by running the program named Dsp029 with the frequency parameters specified by Figure 6 .

Figure 7. Program output for five sinusoids.
missing image

The sinusoids are indistinguishable

Although the actual frequencies of the five cosine functions are significantly different, once they are sampled, they are indistinguishable. Thesampling process converts the actual frequencies to new frequencies that not only fold around one-half the sampling frequency, they also fold around allmultiples of one-half the sampling frequency.

Beginning of the class named Dsp029

The program named Dsp029 is provided in Listing 16 near the end of the module. I will break the program down and explain it in fragments,beginning with the fragment shown in Listing 1 .

Listing 1. Beginning of the class named Dsp029.
class Dsp029 implements GraphIntfc01{ final double pi = Math.PI;//for simplification//Begin default parameters int len = 400;//data lengthint numberSinusoids = 5; //Frequencies of the sinusoidsdouble[] freq = {0.1,0.25,0.5,0.75,0.9};//Amplitudes of the sinusoids double[]amp = {75,75,75,75,75}; //End default parameters

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
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
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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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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