S522, Kewley-Port

Spring, 2008

Assignment #8

**FIR Filters and Window Filter Design**

Specific Assignments from Chap 7 & PWS, Week 8, due 3/5/06

DSPFIRST Problems p. 243,245 **and peznew.zip file (on Oncourse)**

7.5 a & b. For (a), use MatLab poly() or other functions to do the math for you. For (b), look at H(z). Write out all the zeros. Enter them in pezdemo.m and print the display. (do not do 1-c unless you'd like.)

7.9. Write out H(z) for (a). For b, use Matlab to calculate roots for the cacaded system and plot the pole-zero diagram with zplane.m and print it. For c, d & e, use pezdemo.m to enter the zeros on the pole-zero diagram graphically. Print out the corresponding window with the magnitude response, pole-zero for etc.

**DKP Problems using Reading #1Ingle, and pwsmfile.zip files (on Oncourse)**

a. Consider the impluse response in DSPFIRST, Fig 7.16 (see page 237) with {bk} coefficients on page 238. Explain whether it is type 1, 2, 3 or 4. Use the appropriate hr_typeX.m to plot the amplitude reponse and zplane.m for the pole-zero plot (you can alter ex070400 - ex070700.m if you'd like). Use freqz_m.m the magnitude and phase response. Is the relation between the amplitude and magnitude plots what you expect, and does it match Fig. 7.17? Turn in your plots.

b. Starting with hamplot3.m, change it to examine the properties of a Hanning Window. Change the code for M = 45 and determine that it matches p. 249 in PWS. Explain in your own words why it is called a 'raised cosine window'. If we want a small delay, and can accept a transition width of about .3*PI, what value of M can we choose (Table 7.1)? Turn in your Hanning plot for this M.

c. Using Ex. 7.8 (ex070800.m), design a low pass filter using a Hanning window for:

wp = .55*pi Rp = .25dB

ws = .65* pi As = 40dB.

Watch that you have the correct equation to calculate M from Table 7.1,

Turn in your plots of the impluse and magnitude reponse, and your .m code.

d. Use fdatool to complete the design for a Kaiser window specfied in Ex. 7.9. Export your filter from fdatool, and turn in your plot of the magnitude spectrum and a stem plot of your impulse response. Explain if you see any differences with Fig. 7.17 in RWS. Watch that the order "m" in fdatool is different from the number of coefficients - check you symmetry.

{Updated on 2/26/08}