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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Source:  OpenStax, Purdue digital signal processing labs (ece 438). OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10593/1.4
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