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While introducing decomposition , I told you that almost everything we will discuss in this series on DSP is based on the premise that every timeseries can be decomposed into a large number of sinusoids, each having its own amplitude and frequency.

I also introduced the concept of composition , where any time series can be created by adding together the correct set of sinusoids, each having itsown amplitude and frequency.

The notion of sampling analog signals

While signal processing can be accomplished in a variety of ways, including analog processors, digital processors, and optical processors, DSP is based onthe notion that signals in nature can be sampled and converted into a series of numbers. The numbers can be fed into some sort of digital device, which canprocess the numbers to achieve some desired objective.

What is meant by sampling ?

To sample a signal means to measure and record its amplitude at a series of points in time. For example, you might record the temperature in your officeevery ten minutes for twenty-four hours. In this case, the actual temperature in your office would be the analog signal. The 144 temperature values that yourecord would be a sampled time series intended to represent that analog signal.

Uniform sampling is most common

Although uniform sampling is not strictly necessary, in DSP, the most common practice is to sample the signal at uniform intervals of time, (such as once every ten minutes, once per second, or one-thousand times per second). This results in a uniform sampling frequency (sampling rate) .

(Most of the discussions in this series of tutorials on DSP will assume a uniform sampling frequency.)

Some problems arise

While sampled data can be used to simulate most of the signal-processing capabilities available with analog devices, the process of sampling doesintroduce some complications that must be dealt with. For the most part, these complications have to do with the relationship between the sampling frequency (in samples per second) and the highest frequency component contained in the signal (in cycles per second).

Stated simply, if the analog signal contains any sinusoidal components whose frequency is greater than half the sampling frequency, then those componentswill appear in the sampled time series at a different frequency. This can result in a variety of problems.

Reconstruction of the analog signal

Theoretically, if the sampling frequency is twice the highest frequency component contained in the analog signal, then the samples can be used inconjunction with an analog filter to reconstruct the original analog signal.

(However, this requires the construction of a perfect analog filter. In practice, the sampling frequency needs to be perhaps five to ten times thehighest frequency component in the analog signal to make it practical to do a good job of reconstructing the analog signal from the samples.)

Reconstruction is not always required

Once the signal has been sampled and converted to digital form, there is often no interest in reconstructing the analog signal from the samples. Whilethis eliminates the difficulty of reconstruction, it doesn't eliminate the potential problems caused by having the sampling frequency be less than twicethe highest frequency component in the signal.

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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