# 0.2 Lab 2 - discrete-time systems

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## Question or comments

Questions or comments concerning this laboratory should be directedto Prof. Charles A. Bouman, School of Electrical and Computer Engineering, Purdue University, West Lafayette IN 47907;(765) 494-0340; bouman@ecn.purdue.edu

## Introduction

A discrete-time system is anything that takes a discrete-time signal as input and generates a discrete-time signal asoutput. A more general behavioral view of systems is anything that imposes constraints on a set of signals. The concept of a system is very general. It may be used to model the response of an audio equalizer or theperformance of the US economy.

In electrical engineering, continuous-time signals are usually processed by electrical circuits described by differential equations.For example, any circuit of resistors, capacitors and inductors can be analyzed using mesh analysis to yield a system of differentialequations. The voltages and currents in the circuit may then be computedby solving the equations.

The processing of discrete-time signals is performed by discrete-time systems.Similar to the continuous-time case, we may represent a discrete-time system either by a set ofdifference equations or by a block diagram of its implementation. For example, consider the following difference equation.

$y\left(n\right)=y\left(n-1\right)+x\left(n\right)+x\left(n-1\right)+x\left(n-2\right)$

This equation represents a discrete-time system . It operates on the input signal $x\left(n\right)$ to produce the output signal $y\left(n\right)$ . This system may also be defined by a system diagram as in [link] .

Mathematically, we use the notation $y=S\left[x\right]$ to denote a discrete-time system $S$ with input signal $x\left(n\right)$ and output signal $y\left(n\right)$ . Notice that the input and output to the system are the completesignals for all time n . This is important since the output at a particular timecan be a function of past, present and future values of $x\left(n\right)$ .

It is usually quite straightforward to write a computer program to implement a discrete-time system from its difference equation.In fact, programmable computers are one of the easiest and most cost effective ways of implementingdiscrete-time systems.

While equation [link] is an example of a linear time-invariant system, other discrete-time systems may be nonlinear and/or time varying.In order to understand discrete-time systems, it is important to first understand their classificationinto categories of linear/nonlinear, time-invariant/time-varying, causal/noncausal, memoryless/with-memory, and stable/unstable.Then it is possible to study the properties of restricted classes of systems, such as discrete-time systems which are linear, time-invariantand stable.

## Background exercises

Submit these background exercises with the lab report.

## Example discrete-time systems

Discrete-time digital systems are often used in place of analog processing systems.Common examples are the replacement of photographs with digital images, and conventional NTSC TV with directbroadcast digital TV. These digital systems can provide higher quality and/orlower cost through the use of standardized, high-volume digital processors.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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
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?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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