# 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.)

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
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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