# 6.2 Lab 5: prelab

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## Overview

Implementing the narrow-band LPF using an IIR filter is probably the most difficult option to design but the moststraightforward to implement. One reason for the design difficulty stems from the fact that in order to get such asharp response poles close to the unit circle are needed. These poles can then drift outside the unit circle and thesystem can then become unstable when finite precision effects are added. Also, perfectly linear phase (constantgroup delay) cannot be realized using IIR filtering.

There are several approaches to designing an approximatelylinear phase IIR filter. For example, an IIR filter could be run on blocks of samples in both the forward and reversedirection and the results of each block added together; using the filter in both directions would cancel thenonlinear phase response of the filter. Also, iterative design methods exist to design filters that simultaneouslyminimize errors in magnitude and group delay. Yet another approach is to design an IIR filter which approximates thedesired magnitude response (e.g., an elliptic filter using the ellip command in MATLAB) and then design an IIR all-pass filter which compensates for thenonlinear phase. This last approach is the one we will examine here.

## Matlab filter design toolbox

The MATLAB Filter Design (FD) Toolbox contains algorithms used for optimal or near optimal design of filters subjectto various constraints. You can view a description of the toolbox and the functions it contains at this link . The FD Toolbox will be installed on the white Dell machinenearest the door in the ECE 320 lab.

## Using the filter design toolbox

Although it is possible to design a very good LPF magnitude response using an elliptic filter, we do not have theadvantage with the ellip command of being able to constrain the poles away from the unit circleto prevent instability. Fortunately, the FD Toolbox provides a command called iirlpnormc which allows us to keep the poles within a circle of a specified radius. Note that this command implements aleast- $p$ 'th algorithm. The term least- $p$ 'th signifies that the algorithm attempts to minimize a ${L}_{p}$ -norm error. In the case of the magnitude response, the ${L}_{p}$ -norm error is given as

$({\left|H\right|}_{p}, {\frac{1}{\mathrm{2\pi }}\int_{-\pi }^{\pi } {\left|H(\omega )-{H}_{d}(\omega )\right|}^{p}W(\omega )\,d \omega }^{\frac{1}{p}})$

where $H$ is the actual frequency response, ${H}_{d}$ is the desired response, and $W$ is some weighting function. Most of the time the weighting function used isone which equals 1 over the passband and stop-band and 0 in the transition band. The role of $W$ in the above equation is similar to that used in FIR filter design( remez ). The relative weights in the stop-band and pass-band are set by $W$ and control the relative magnitude of the ripples in these bands. Note thatminimizing the ${L}_{2}$ -norm is equivalent to minimizing the RMS error in the magnitude.In contrast, the ${L}_{\infty }$ -norm is equivalent to minimizing the maximum error over thefrequencies of interest (why?). In this lab we areconcerned with minimizing the ${L}_{\infty }$ -norm. Of course, we cannot use infinity in any of our computationsso using a large number (e.g. 128) must suffice.

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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
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it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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