# 2.1 Dsp00104-sampled time series  (Page 5/10)

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## What happens when the sampling frequency is reduced ?

As you can see in these figures, regardless of which graphical treatment you use, the sampling frequency relative to the signal frequency is sufficientlyhigh to present a respectable view of the sinusoidal signals. Now I'm going to show you what happens when the sampling frequency is reduced without changingthe frequency of the sinusoids.

Figure 5 shows the same five sinusoids as above, except that they are plotted across a longer period of time. (The presentation in Figure 5 treats each sample as a rectangle.)

Figure 5. Five sampled sinusoids

In particular, you should note the obvious frequency difference between the top sinusoid and the bottom sinusoid. Also note the frequency difference betweenthe two sinusoids immediately above and immediately below the center sinusoid.

## Some numbers

Let's put some numbers to the frequencies involved. If we consider the sampling frequency to be 20 samples per second, then the center sinusoid has afrequency of one cycle per second, with 20 samples per cycle. On that basis, the frequencies of the sinusoids from top to bottom are as shown below:

```1.75 cycles per second 1.50 cycles per second1.00 cycles per second 0.50 cycles per second0.25 cycles per second```

## Comparison of frequencies with center frequency

The most important thing to note about these frequency values is how the four outer frequencies relate to the center frequency. The top and bottom frequencyvalues differ from the center frequency by 0.75 cycles per second. In other words, the frequency of the top sinusoid is 0.75 cycles per second above thefrequency of the center sinusoid, and the frequency of the bottom sinusoid is 0.75 cycles per second below the frequency of the center sinusoid.

Similarly, the second and fourth frequency values differ from the center frequency by 0.50 cycles per second. Again, one is above and the other is below.

## Reduce the sampling frequency

What I am going to do now is to recalculate and re-plot the values for each sinusoid at a sampling frequency of two samples per second instead of 20 samplesper second. This will place the frequency of the center sinusoid exactly at the folding frequency of one cycle per second. More importantly, this will place thefrequencies of the top two sinusoids above the folding frequency.

## Re-plot the sampled data

I will re-plot the data for each sinusoid across the same period of time as in Figure 5 . The results are shown in Figure 6 . It would probably be useful for you to view Figure 5 and Figure 6 side-by-side in separate browser windows.

Figure 6. Result of re-sampling the five sinusoids.

There are several important things to note about Figure 6 .

## Center plot no longer resembles a sinusoid

First, you will probably notice that the plot for the center sinusoid no longer looks much like a sinusoid. Rather, it looks like a square wave. This isthe result of having exactly two samples per cycle of the sinusoid. One sample is taken from the positive lobe of the sinusoid, and the next sample is takenfrom the negative lobe of the sinusoid. This pattern repeats, producing something that looks like a square wave. (A different graphical treatment would make it look like a triangular wave.)

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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
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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
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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?
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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