# 0.6 Lab 5b - digital filter design (part 2)  (Page 5/6)

 Page 5 / 6

The outputs of the command are n = filter length - 1 , and the vectors fo , mo , and w which are intermediate filter parameters.

Once the filter length, n , is obtained, the Matlab command for designing a Parks-McClellan filteris b = firpm(n,fo,mo,w) . The inputs n , fo , mo , and w are the corresponding outputs of firpmord , and the output b is a vector of FIR filter coefficients such that

$H\left(z\right)=b\left(1\right)+b\left(2\right){z}^{-1}+\cdots +b\left(n+1\right){z}^{-n}$

(What is the impulse response of this filter?)

For further information, read the help document on using Matlab to implement the Parks-McClellan algorithm.

Now design a symmetric FIR filter using firpmord and firpm in Matlab to meet the design specifications given in the "Filter Design Using the Kaiser Window" section. Compute the DTFT of the filter's response for at least 512 points,and use this result to compute the passband and stopband ripple of the filter that was designed.Adjust the filter length until the minimum order which meets the design constraints is found.Plot the magnitude of the DTFT in dB of the final filter design.

## Inlab report

Do the following:
1. Submit the final measured values of filter length, passband ripple, and stopband ripple.How accurate was the filter order computation using Matlab's firpmord ? How does the length of this filter compare to the filterdesigned using a Kaiser window?
2. Submit the plot of the filter's DTFT. How does the frequency response of the Parks-McClellan filtercompare to the filter designed using the Kaiser window? Comment on the shape of both the passband and stopband.

Use the filter you have designed to remove the noise from the signal nspeech2.mat . Play the noisy and filtered speech signals back using sound and listen to them carefully. Compute theDTFT of 400 samples of the filtered signal starting at time $n=20,001$ (i.e. 20001:20400 ).Plot the magnitude of the DTFT in decibels versus frequency in radians for $|\omega |<\pi$ . Compare this with the spectrum of the noisy speech signal shownin [link] , and also with the magnitude of the DTFT of the Kaiser filtered signal.

Submit the plot of the DTFT magnitude for the filtered signal. Comment on how the audio qualityof the signal changes after filtering. Also comment on any differences in audio quality between the Parks-McClellan filteredspeech and the Kaiser filtered speech.

## Design of discrete-time iir filters using numerical optimization

In this section, we consider the design of discrete-time IIR filters through the direct search of filter parametersthat will minimize a specific design criterion. Such “brute force” approaches to filter design have becomeincreasingly more popular due to the wide availability of high speed computers and robust numerical optimization methods.

Typically, numerical approaches to filter design have two parts. First, they design a cost , or error criterion. This criterion is a measure of the difference betweenthe ideal filter response and the response of the computed or “approximate” filter. The goal is to findthe approximate filter with the lowest cost (error). Mean square error isa popular cost criterion. The second part is to minimize the cost with respect to the filter parameters.We will perform the required numerical optimization with the fminsearch function in Matlab's Optimization Toolbox .

#### Questions & Answers

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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
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
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!