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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


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
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
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Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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