<< Chapter < Page
  Digital signal processing - dsp     Page 9 / 10
Chapter >> Page >
What happened to the peak structure:

In case you are wondering why the peaks in Figure 9 have less structure than the peaks in Figure 7 , this is because the points at which I computed the spectral data in Figure 9 were twice as far apart as the points at which I computed the spectral data in Figure 7 .

(The total frequency range in Figure 9 is twice as wide as in Figure 7 , but I computed the same number of points in both cases.)

Although it's not obvious at this plotting scale, there are zero-valued points between the side lobes on the peaks in Figure 7 .

The points in the spectral display of Figure 9 simply missed the side lobes and hit the zeros between the side lobes. I willhave a lot more to say about this in a future module discussing spectral analysis.

Back to the case with the sampling problem

Now let's take another look at the case with the sampling problem. This is the case where the sampling frequency was reduced from four samples per secondto two samples per second but the frequencies of the sinusoids was not changed. This view of the problem is shown in Figure 10 . It will probably be useful for you to compare Figure 10 with Figure 8 .

Figure 10. Spectral analyses of five sinusoids with sampling problem
missing image

Folding frequency is at the center

As with the previous case, each of the plotted spectra in Figure 10 shows the frequency range from zero frequency to the sampling frequency of two samples persecond. The folding frequency of one cycle per second appears in the center of each plot.

Peaks to left correspond to Figure 8

The peaks to the left of center in Figure 10 correspond to the peaks in Figure 8 . Because the right edge of Figure 8 is the folding frequency, the peaks to the right of center in Figure 10 don't appear in Figure 8 .

A mirror image

As is always the case, everything to the right of the folding frequency in Figure 10 is a mirror image of everything to the left of the folding frequency.

I have identified the artifacts created by the sampling process with a red oval in Figure 10 .

Raw data frequency exceeds folding frequency

The problem, as you will recall, is that the frequency of the sinusoids corresponding to the two bottom plots in Figure 10 is above the folding frequency. Thus the peaks to the right of center in the bottom two plots of Figure 10 actually represent the frequencies of the corresponding sinusoids.

Unfortunately, these two peaks appear to the right of the folding frequency, which the area of the spectra that we normally ignore.

Artifacts to the left of the folding frequency

Furthermore, these two peaks are reflected through the folded mirror image process into the area to the left of the folding frequency. For these twosinusoids, the peaks to the left of the folding frequency are artifacts, and I have identified them as such with ovals.

Normally can't identify artifacts

I am able to identify these two peaks as artifacts only because I know the true frequency makeup of the raw data. In most real-world situations withunknown data, there would be no way for me to identify these particular peaks to the left of the folding frequency as artifacts.

Questions & Answers

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
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
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing - dsp' conversation and receive update notifications?