# 2.1 Dsp00104-sampled time series  (Page 3/10)

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## The Nyquist folding frequency

If the analog signal contains frequency components that are greater than half the sampling frequency, those components will appear to be at a differentfrequency in the sampled data.

The frequency that is equal to half the sampling frequency is often referred to as the Nyquist folding frequency , or simply the folding frequency. The folding frequency is half the sampling frequency. I will provide exampleslater to illustrate where this frequency gets its name.

## A brief description

If a frequency component in the analog signal is less than the sampling frequency, but exceeds the folding frequency by an amount d , it will appear in the sampled data at a frequency that is the folding frequency minus d .

In other words, the entire frequency spectrum appears to fold around the folding frequency such that all frequency components that are above the folding frequency fold down to a similar position on the lower side of the foldingfrequency. Those frequency components above the folding frequency produce a mirror image below the folding frequency.

(If a frequency component in the analog signal is greater than the sampling frequency, folding still occurs, but in a more complicated way.)

## Some specific numbers

Some specific numbers may make this easier to understand. Assume that the sampling frequency is 2000 samples per second, giving a folding frequency of1000 cycles per second.

If an analog signal contains a frequency component at 1100 cycles per second, it will fold down and appear at 900 cycles per second in the sampled signal.

A frequency component at 1600 cycles per second in the analog signal will fold down and appear at 400 cycles per second in the sampled signal.

A frequency component at 2000 cycles per second (the sampling frequency) will fold down and appear at zero frequency in the sampled signal.

The folding behavior is fairly easy to illustrate graphically, and I will do that shortly. Before doing that, however, I need to make a few comments aboutwhat it really means to sample an analog signal.

## What do we really have ?

First we need to think about what we really have when we have a sampled time series. All that we really have is a set of values taken at specific times. Inreality, we know nothing about the values that actually existed for the analog signal in-between the samples.

For example, in the temperature experiment described earlier, when we record the temperature once every ten minutes, we can't really say what values we wouldhave recorded if we had recorded the temperature once every five minutes instead. Therefore, we sometimes find ourselves estimating what the values arebetween the recorded samples.

## Sampled sinusoids

Consider the five plots shown in Figure 1 .

Figure 1. Samples from five different sinusoids.

Figure 1 shows the values for samples taken from five different sinusoids (the height of each vertical bar represents the value of a sample).

All five sinusoids were sampled at the same sampling frequency. The sinusoid in the center was sampled twenty times per cycle (not necessarily twenty times per second).

#### Questions & Answers

what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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?
what is a peer
What is meant by 'nano scale'?
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
what is Nano technology ?
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
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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