# 0.6 Digital filtering and the dft  (Page 11/13)

 Page 11 / 13

The general form of an IIR filter is

$\begin{array}{cc}\hfill y\left[k+1\right]=& {a}_{0}y\left[k\right]+{a}_{1}y\left[k-1\right]+...+{a}_{n}y\left[k-n\right]+\hfill \\ & {b}_{0}x\left[k\right]+{b}_{1}x\left[k-1\right]+...+{b}_{m}x\left[k-m\right],\hfill \end{array}$

which can be rewritten more concisely as

$y\left[k+1\right]={a}^{T}y\left[k\right]+{b}^{T}x\left[k\right]$

where

$\begin{array}{cc}\hfill a& ={\left[{a}_{0},{a}_{1},...,{a}_{n}\right]}^{T}\hfill \\ \hfill b& ={\left[{b}_{0},{b}_{1},...,{b}_{m}\right]}^{T}\hfill \end{array}$

are column vectors of the parameters of the filter and where

$\begin{array}{cc}\hfill x\left[k\right]& ={\left[x\left[k\right],x\left[k-1\right],...,x\left[k-m\right]\right]}^{T}\hfill \\ \hfill y\left[k\right]& ={\left[y\left[k\right],y\left[k-1\right],...,y\left[k-n\right]\right]}^{T}\hfill \end{array}$

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= $\left[{b}_{0},{b}_{1},...,{b}_{m}\right]$ and a= $\left[1,-{a}_{0},-{a}_{1},...,-{a}_{n}\right]$ . 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

$x\left[k\right]=\frac{1}{b}r\left[k\right]-\frac{a}{b}r\left[k-1\right].$

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.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
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
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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?
what is a peer
What is meant by 'nano scale'?
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 ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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
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