# 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).

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
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
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
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 ?
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
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