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The two sinusoids above the center had higher frequencies than the sinusoid in the center, with the sinusoid at the top having the highest frequency. For afixed sampling frequency, the sinusoids above the center had fewer samples per cycle than the sinusoid in the center. The sinusoid at the top had the fewestnumber of samples per cycle.

The two sinusoids below the center had lower frequencies, than the sinusoid in the center, with the sinusoid at the bottom having the lowest frequency. Thetwo sinusoids below the center had more samples per cycle than the sinusoid in the center. The sinusoid at the bottom had the most samples per cycle.

The number of samples per cycle is important

In the final analysis, what really counts is not the number of samples per second of the sampling frequency, or the number of cycles per second of thesignal frequency. What really counts is the number of samples per cycle of the highest frequency component. This value is established by the combination of the signal frequency and the samplingfrequency.

The values between the samples

Because the plots in Figure 1 are pure sinusoids, I can mathematically determine the values between the samples. However, if there had been theslightest amount of random noise superimposed on the sinusoids, (which is the more realistic situation), I would have no way of knowing the values between the samples. Thus, all of the information that I have about these five signalsis contained in the heights of the vertical bars shown in Figure 1 .

Estimating the values in between the samples

As mentioned earlier, we often find ourselves estimating the values in between the samples. One way to do this is shown in Figure 2 , which shows a different graphical treatment for the same five sinusoids.

Figure 2. Rectangular representations of samples from five sinusoids.
missing image

Figure 2 represents each of the sample values as a rectangle. In effect, this treatment estimates that there is no change in the value of the analog signalfor half a sample interval after the sample is taken. Then the value of the analog signal jumps to the value of the next sample.

A more common representation

Now consider the graphical treatment for the same five sinusoids shown in Figure 3 .

Figure 3. Trapezoidal representations of samples from five sinusoids.
missing image

Figure 3 shows a more common representation of the data. Figure 3 treats each sample as a trapezoid consisting of a rectangle and a right triangle. Thetriangle sets atop the rectangle and connects each sample value to the next with a straight line.

The most common representation

Now consider the most common representation of the sampled data, as shown in Figure 4 .

Figure 4. Most common representations of samples from five sinusoids.
missing image

Figure 4 shows the most common representation of the sampled data. Figure 4 is the same as Figure 3 except that the vertical lines that identify the sides of the trapezoids have been omitted. In Figure 4 , each sample value is connected to the next sample value with a straight-line segment.

Questions & Answers

what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
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?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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