<< Chapter < Page Chapter >> Page >

Plot the rectangular, Hamming, Hanning, and Blackman window functions of length 21 on a single figure using the subplot command. You may use the Matlab commands hamming , hann , and blackman . Then compute and plot the DTFT magnitude of each of the four windows.Plot the magnitudes on a decibel scale (i.e., plot 20 log 10 | W ( e j ω ) | ). Download and use the function DTFT.m to compute the DTFT.

Use at least 512 sample points in computing the DTFT by typing the command DTFT(window,512) . Type help DTFT for further information on this function.

Measure the null-to-null mainlobe width (in rad/sample) and the peak-to-sidelobe amplitude (in dB)from the logarithmic magnitude response plot for each window type. The Matlab command zoom is helpful for this. Make a table with these values and the theoretical ones.

Now use a Hamming window to design a lowpass filter h ( n ) with a cutoff frequency of ω c = 2 . 0 and length 21. Note: You need to use [link] and [link] for this design. In the same figure, plot the filter's impulse response, and the magnitude of the filter's DTFT in decibels.

Inlab report

  1. Submit the figure containing the time domain plots of the four windows.
  2. Submit the figure containing the DTFT (in decibels) of the four windows.
  3. Submit the table of the measured and theoretical window spectrum parameters.Comment on how close the experimental results matched the ideal values. Also commenton the relation between the width of the mainlobe and the peak-to-sidelobe amplitude.
  4. Submit the plots of your designed filter's impulse response and the magnitude of the filter's DTFT.

Filter design using the kaiser window

Download nspeech2.mat for the following section.

Tolerance specifications for the frequency response of a filter.

The standard windows of the "Filter Design Using Standard Windows" section are an improvement over simple truncation,but these windows still do not allow for arbitrary choices of transition bandwidth and ripple.In 1964, James Kaiser derived a family of near-optimal windows that can be used to design filters which meet or exceed any filter specification.The Kaiser window depends on two parameters: the window length N , and a parameter β which controls the shape of the window. Large values of β reduce the window sidelobes and therefore result in reduced passband and stopband ripple.The only restriction in the Kaiser filter design method is that the passband and stopband ripple must be equal in magnitude.Therefore, the Kaiser filter must be designed to meet the smaller of the two ripple constraints:

δ = min { δ p , δ s }

The Kaiser window function of length N is given by

w ( n ) = I 0 β n ( N - 1 - n ) N - 1 I 0 ( β ) n = 0 , 1 , ... , N - 1 0 otherwise

where I 0 ( · ) is the zero'th order modified Bessel function of the first kind, N is the length of the window, and β is the shape parameter.

Kaiser found that values of β and N could be chosen to meet any set of design parameters, ( δ , ω p , ω s ) , by defining A = - 20 log 10 δ and using the following two equations:

β = 0 . 1102 ( A - 8 . 7 ) A > 50 0 . 5842 ( A - 21 ) 0 . 4 + 0 . 07886 ( A - 21 ) 21 A 50 0 . 0 A < 21
N = 1 + A - 8 2 . 285 ( ω s - ω p )

where · is the ceiling function, i.e. x is the smallest integer which is greater than or equal to x .

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Purdue digital signal processing labs (ece 438). OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10593/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Purdue digital signal processing labs (ece 438)' conversation and receive update notifications?

Ask