<< Chapter < Page Chapter >> Page >

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

This is the first part of a two week laboratory in digital filter design.The first week of the laboratory covers some basic examples of FIR and IIR filters, and then introduces the conceptsof FIR filter design. Then the second weekcovers systematic methods of designing both FIR and IIR filters.

Background on digital filters

In digital signal processing applications, it is often necessary to change the relative amplitudesof frequency components or remove undesired frequencies of a signal.This process is called filtering . Digital filters are used in a variety of applications.In Laboratory 4, we saw that digital filters may be used in systems that perform interpolation and decimationon discrete-time signals. Digital filters are also used in audio systemsthat allow the listener to adjust the bass (low-frequency energy) and the treble (high frequency energy) of audio signals.

Digital filter design requires the use of both frequency domain and time domain techniques.This is because filter design specifications are often given in the frequency domain, but filters are usually implementedin the time domain with a difference equation. Typically, frequency domain analysis is done using the Z-transform andthe discrete-time Fourier Transform (DTFT).

In general, a linear and time-invariant causal digital filter with input x ( n ) and output y ( n ) may be specified by its difference equation

y ( n ) = i = 0 N - 1 b i x ( n - i ) - k = 1 M a k y ( n - k )

where b i and a k are coefficients which parameterize the filter. This filter is said to have N zeros and M poles. Each new value of the output signal, y ( n ) , is determined by past values of the output, and by present and past valuesof the input. The impulse response, h ( n ) , is the response of the filter to an input of δ ( n ) , and is therefore the solution to the recursive difference equation

h ( n ) = i = 0 N - 1 b i δ ( n - i ) - k = 1 M a k h ( n - k ) .

There are two general classes of digital filters: infinite impulse response (IIR) and finite impulse response (FIR).The FIR case occurs when a k = 0 , for all k . Such a filter is said to have no poles, only zeros.In this case, the difference equation in [link] becomes

h ( n ) = i = 0 N - 1 b i δ ( n - i ) .

Since [link] is no longer recursive, the impulse response has finite duration N .

In the case where a k 0 , the difference equation usually represents an IIR filter.In this case, [link] will usually generate an impulse response which has non-zero values as n . However, later we will see that for certain valuesof a k 0 and b i , it is possible to generate an FIR filter response.

The Z-transform is the major tool used for analyzing the frequency response of filters and their differenceequations. The Z-transform of a discrete-time signal, x ( n ) , is given by

X ( z ) = n = - x ( n ) z - n .

where z is a complex variable. The DTFT may be thought of as a special case of the Z-transformwhere z is evaluated on the unit circle in the complex plane.

Questions & Answers

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
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
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Purdue digital signal processing labs (ece 438)' conversation and receive update notifications?

Ask