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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
ya I also want to know the raman spectra
Bhagvanji
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, 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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