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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 ( n ) = y ( n - 1 ) + x ( n ) + x ( n - 1 ) + x ( n - 2 )

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

Diagram of a discrete-time system. (D = unit delay)

Mathematically, we use the notation y = S [ x ] to denote a discrete-time system S with input signal x ( n ) and output signal y ( n ) . 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 ( n ) .

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

The phenomenon by which Protoplasm of a cell shrinks from the wall is 
test Reply
which vein connective from harm to Brian
Burton Reply
which nevel succulate blood system from harm to hear
Burton
if an organism is cartilaginous is fully capable of a protecting the internal organs
Verah Reply
what is different between cell and tissue
Rose Reply
cell is the functional and structural unit of life while tissue is a group of cells aggregate to perform a similar or particular function
Tajudeen
cell is the basic unit of life while tissue is group of related cells that perform the same function Eg. the nerve tissue is made up of nerve cells
AAGifty
please what is meant by mutation
Kyere Reply
mutation is the change in DNA which results in the evolution
Shshank
what is binominal nomenclature?
Furaha Reply
the system of naming organisms depending on their xtics of origin
Vincent
The system of naming organisms using two-words Latin names
Agyeiwaa
what is the fate of reduced NAD in cell metabolism
namirembe Reply
what is plant cell
OLUWAKEMI Reply
what is the importance of meoisis
Kamasa Reply
it also aids in formation of pollen grain in anther and formation of ovules in ovary of flowering plant
Orawo
it also aids in formation of sperm or ova in animals
Orawo
explain the function of the skeleton
Jonathan Reply
skeleton is mainly the infrastructure of the organisms
Shshank
what 's different between immunity and vaccination
Symon Reply
vaccination simply refers to as drugs usually injected,most times in a liquid form given to a person or an animal,while immunity refers to a source of prevention usually in a liquid form that help in disease prevention
Grace
In children
Grace
Golgi apparatus helps in the formation of lysosomes
Diana
what is the difference between placenta and umbilical cord?
Grace Reply
No difference
Onwane
what's golgi apparatus.
Grace
What is biology
Rita Reply
is the study of living things
Kisa
biology is the study of living and non living things
Tinta
Biology is the study of living things
Addai
the study of living organisms
Furaha
Biology is the study of living organism or things
Rose
Biology is the study of both living and non living things
Funteh
distinguish between sex linked characters and sex limited characters
Kisa Reply
what is active transport
Jessy Reply
why is diffusion important
Jessy
dissolved substance move with in the cytoplasm by diffusion
Kisa
what role does mutation play in the process of evolution
Kisa
active transport refers to the movement of certain molecules or substances from lower to higher concentration with the help of energy or ATP
Shshank
mutation occurs due to change in DNA and DNA forms our body & if DNA changes then our body also acquire some changes & these changes gradually leads to the evolution of new species
Shshank
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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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