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This module discusses the theory and practical considerations behind the use of discrete time tools to process of continuous time signals.

Introduction

Digital computers can process discrete time signals using extremely flexible and powerful algorithms. However, most signals of interest are continuous time signals, which is how data almost always appears in nature. Now that the theory supporting methods for generating a discrete time signal from a continuous time signal through sampling and then perfectly reconstructing the original signal from its samples without error has been discussed, it will be shown how this can be applied to implement continuous time, linear time invariant systems using discrete time, linear time invariant systems. This is of key importance to many modern technologies as it allows the power of digital computing to be leveraged for processing of analog signals.

Discrete time processing of continuous time signals

Process structure

With the aim of processing continuous time signals using a discrete time system, we will now examine one of the most common structures of digital signal processing technologies. As an overview of the approach taken, the original continuous time signal x is sampled to a discrete time signal x s in such a way that the periods of the samples spectrum X s is as close as possible in shape to the spectrum of X . Then a discrete time, linear time invariant filter H 2 is applied, which modifies the shape of the samples spectrum X s but cannot increase the bandlimit of X s , to produce another signal y s . This is reconstructed with a suitable reconstruction filter to produce a continuous time output signal y , thus effectively implementing some continuous time system H 1 . This process is illustrated in [link] , and the spectra are shown for a specific case in [link] .

A block diagram for processing of continuous time signals using discrete time systems is shown.

Further discussion about each of these steps is necessary, and we will begin by discussing the analog to digital converter, often denoted by ADC or A/D. It is clear that in order to process a continuous time signal using discrete time techniques, we must sample the signal as an initial step. This is essentially the purpose of the ADC, although there are practical issues that which will be discussed later. An ADC takes a continuous time analog signal as input and produces a discrete time digital signal as output, with the ideal infinite precision case corresponding to sampling. As stated by the Nyquist-Shannon Sampling theorem, in order to retain all information about the original signal, we usually wish sample above the Nyquist frequency ω s 2 B where the original signal is bandlimited to ( - B , B ) . When it is not possible to guarantee this condition, an anti-aliasing filter should be used.

The discrete time filter is where the intentional modifications to the signal information occur. This is commonly done in digital computer software after the signal has been sampled by a hardware ADC and before it is used by a hardware DAC to construct the output. This allows the above setup to be quite flexible in the filter that it implements. If sampling above the Nyquist frequency the. Any modifications that the discrete filter makes to this shape can be passed on to a continuous time signal assuming perfect reconstruction. Consequently, the process described will implement a continuous time, linear time invariant filter. This will be explained in more mathematical detail in the subsequent section. As usual, there are, of course, practical limitations that will be discussed later.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
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