# 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.

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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