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S ( f ) = 1 T s X f .

Notice that the reconstructed signal is scaled by the factor 1 T s .

Of course, the sample-and-hold does not generate perfect impulses. Instead it generates a pulseof width T s , and magnitude equal to the input sample. Therefore, the new signal out of the sample-and-holdis equivalent to the old signal (an impulse train) convolved with the pulse

p ( t ) = rect t T s - 1 2 .

Convolution in the time domain is equivalent to multiplication in the frequency domain,so this convolution with p ( t ) is equivalent to multiplying by the Fourier transform P ( f ) where

| P ( f ) | = T s | sinc ( f / f s ) | .

Finally, the magnitude of the frequency response of the N -th order Butterworth filter is given by

| H b ( f ) | = 1 1 + f f c N .

We may calculate the complete magnitude response of the sample-and-hold system by combining the effects of the Butterworth filters in [link] , the ideal sampling system in [link] , and the sample-and-hold pulse width in [link] . This yields the final expression

| H ( f ) | = | H b ( f ) P ( f ) 1 T s H b ( f ) | = 1 1 + f f c N 2 | sinc ( f / f s ) | .

Notice that the expression | sinc ( f / f s ) | produces a roll-off in frequency which will attenuate frequencies close to the Nyquistrate. Generally, this roll-off is not desirable.

Inlab report

Do the following using T s = 1 sec, f c = 0 . 45 Hz, and N = 20 . Use Matlab to produce the plots (magnitude only), for frequencies in therange: f = -1:.001:1 .
  • Compute and plot the magnitude response of the system in [link] without the sample-and-hold device.
  • Compute and plot the magnitude responseof the complete system in [link] .
  • Comment on the shape of the two magnitude responses. How might the magnitude response of the sample-and-hold affectthe design considerations of a high quality audio CD player?

Simulink utilities for lab 4.

In this lab we will use Simulink to simulate the effects of the sampling and reconstruction processes.Simulink treats all signals as continuous-time signals. This means that “sampled” signals are really just continuous-time signals that contain a series offinite-width pulses. The height of each of these pulses is the amplitude of the input signal at the beginning of the pulse. In other words, boththe sampling action and the zero-order-hold reconstruction are done at the same time; the discrete-time signal itself is never generated.This means that the impulse-generator block is really a “pulse-generator”, or zero-order-hold device. Remember that, in Simulink,frequency spectra are computed on continuous-time signals. This is why many aliasedcomponents will appear in the spectra.

Sampling and reconstruction using an impulse generator

For help on the following topics select the corresponding links: simulink and printing figures in simulink . For the following section, download the file Lab4Utils.zip .

In this section, we will experiment with the sampling and reconstruction of signals using a pulse generator.This pulse generator is the combination of an ideal impulse generator and a perfect zero-order-hold device.

In order to run the experiment, first download the required Lab4Utilities . Once Matlab is started, type “Lab4”.A set of Simulink blocks and experiments will come up as shown in [link] .

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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