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Illustrates the folding frequency

Hopefully this illustration will make the concept of the folding frequency easier for you to understand. The folding frequency is one-half the samplingfrequency. The entire spectrum below the folding frequency folds around the folding frequency and the peaks in that spectrum appear in mirror-image formatabove the folding frequency.

The frequency information for all frequency components above the folding frequency is lost when the signal is sampled. In addition, the energy associatedwith those components will fold around and can corrupt the information for frequency components that are below the folding frequency.

The bottom line

The bottom line is that you must be very careful when sampling analog signals for later processing using DSP. In order to avoid erroneous results, you mustsample sufficiently fast to ensure that your sampling rate is greater than twicethe highest frequency components contained in the analog signal.

On the other hand, the greater your sampling rate, the more computer-intensive will be most of the DSP techniques that you apply to the datalater. For economy reasons, therefore, you don't want your sampling frequency to be excessively high.

Using an analog low-pass pre-filter

A common approach to sampling is to feed the analog signal into an analog-to-digital (AtoD) converter. This is a device that measures the amplitude of the analog signal at a uniform sampling frequency. It is commonpractice to place a low-pass analog filter immediately ahead of the converter to suppress any analog frequency components that are greater than one-half thesampling frequency.

Digital re-sampling

Another common approach is to initially sample the analog signal at a sufficiently high rate to ensure that the sampling rate is greater than twicethe highest frequency contained in the analog signal. Then, if you really don't need all of that high-frequency information, you can apply a low-pass digitalfilter to suppress the high-frequency energy. Then you can re-sample the data to a lower sampling frequency simply by discarding samples. The data with the lowersampling frequency can then be used for further DSP analysis.

Summary

I explained the meaning of sampling, and explained some of the problems that arise when sampling and processing analog signals.

The problems generally relate to the relationship between the sampling frequency and the high-frequency components contained in the analog signal.

I explained the concept of the Nyquist folding frequency, which is half the sampling frequency.

I illustrated the frequency folding phenomena by plotting sampled time series data as well as spectral data.

Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: Dsp00104: Digital Signal Processing (DSP) in Java, Sampled Time Series
  • File: Dsp00104.htm
  • Published: 10/04/02

Baldwin explains the meaning of sampling, and identifies some of the problems that arise when sampling and processing analog signals. He explains the concept of the Nyquist folding frequency and illustrates the folding phenomena by plotting time series data as well as spectral data.

Disclaimers:

Financial : Although the Connexions site makes it possible for you to download a PDF file for thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing me as the author. Ineither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, please beaware that it is a copy of a module that is freely available on cnx.org and that it was made and published withoutmy prior knowledge.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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da
Application of nanotechnology in medicine
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RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
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What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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Damian Reply
what king of growth are you checking .?
Renato
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?
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
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biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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