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The general form of an IIR filter is

y [ k + 1 ] = a 0 y [ k ] + a 1 y [ k - 1 ] + . . . + a n y [ k - n ] + b 0 x [ k ] + b 1 x [ k - 1 ] + . . . + b m x [ k - m ] ,

which can be rewritten more concisely as

y [ k + 1 ] = a T y [ k ] + b T x [ k ]


a = [ a 0 , a 1 , . . . , a n ] T b = [ b 0 , b 1 , . . . , b m ] T

are column vectors of the parameters of the filter and where

x [ k ] = [ x [ k ] , x [ k - 1 ] , . . . , x [ k - m ] ] T y [ k ] = [ y [ k ] , y [ k - 1 ] , . . . , y [ k - n ] ] T

are vectors of past input and output data. The symbol z T indicates the transpose of the vector z . In M atlab , transpose is represented using the single apostrophe ' , but take care: when using complex numbers, the apostrophe actually implements a complex conjugateas well as transpose.

M atlab has a number of functions that make it easy to explore IIR filtering.For example, the function impz plots the impulse response of a discrete IIR (or FIR) filter.The impulse response of the system [link] is found by entering b=1; a=[1, -0.8]; impz(b,a) The parameters are the vectors b= [ b 0 , b 1 , . . . , b m ] and a= [ 1 , - a 0 , - a 1 , . . . , - a n ] . Hence the above code gives the responsewhen a of [link] is + 0 . 8 . Similarly, the command freqz(b,a) displays the frequency response for the IIR filter where b and a are constructed in the same way.

The routine waystofiltIIR.m explores ways of implementing IIR filters. The simplest method uses the filter command. For instance filter(b,a,d) filters the data d through the IIR system with parameters b and a defined as above. This gives the same output as first calculating the impulse response h and then using filter(h,1,d) . The fastest (and most general) way to implement the filter is in the for loop at the end, which mimics the time domain method for FIR filters, but includes the additionalparameters a .

a=[1 -0.8]; lena=length(a)-1;       % autoregressive coefficientsb=[1]; lenb=length(b);              % moving average coefficientsd=randn(1,20);                      % data to filter if lena>=lenb,                      % dimpulse requires lena>=lenb   h=impz(b,a);                      % impulse response of filter  yfilt=filter(h,1,d)               % filter x[k] with h[k]end yfilt2=filter(b,a,d)                % filter directly using a and by=zeros(lena,1); x=zeros(lenb,1);   % initial states in filter for k=1:length(d)-lenb              % time domain method  x=[d(k);x(1:lenb-1)];             % past values of inputs  ytim(k)=-a(2:lena+1)*y+b*x;       % directly calculate y[k]   y=[ytim(k);y(1:lena-1)];          % past values of outputs end
waystofiltIIR.m ways to implement IIR filters (download file)

Like FIR filters, IIR filters can be lowpass, bandpass, highpass, or can have almost any imaginableeffect on the spectrum of its input.

Some IIR filters can be used as inverses to some FIR filters. Show that the FIR filter

x [ k ] = 1 b r [ k ] - a b r [ k - 1 ] .

is an inverse of the IIR filter [link] .

FIR filters can be used to approximate the behavior of IIR filters by truncating the impulse response.Create a FIR filter with impulse response given by the first 10 terms of [link] for a = 0 . 9 and b = 2 . Simulate the FIR filter and the IIRfilter [link] in M atlab , using the same random input to both. Verify that the outputsare (approximately) the same.

Questions & Answers

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
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
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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