IIR filter.Can someone guides me?

[scdoro]

Hi all,

Can someone help me with this design question, i have worked out the steps to do the problem.
Can someone help me scanned through it and see if i missed out anything.
Qn) what should be the reasonable value which i should choose for 'fp in "step 2"?


steps:
1) Required to find the prototype lowpass cutoff frequency for 'fp and 'fs.
*2) Choose a reasonable value for 'fp
3) Obtain alpha1 and alpha2 by substituting 'fp,Wup,wlp values into the four equations
4) Now, we can obtain 'fs since alpha1,alpha2,Wus,wls values are found and given
5) Compute the analog butterworth lowpass prototype specification
6) Design Analog butterworth lowpass filter
7) Perform billinear transformation to obtain digital lowpass butterworth filter
7) Transform digital lowpass to bandstop using the frequency band transformation


thanks

regards
scdoro[/u]

 

[mehtesham]

see this:

 

[Kral]

scdoro,
You have omitted one step: prior to performing the bilinear transformation, you must pre-warp the critical frequencies of your analog prototype filter to account for the frequency distortion that is inherent in the bilinear transformation. If you use the impulse invariant method, this step, of course, is not required.
Regards,
Kral

 

[scdoro]

hi kral,

thanks for the reminder.

Do you know what reasonable values i should take for fp'? The passband frequency of the prototype lowpass filter.

Another issue which i will like to confirm is that is ωu and ωl referring to these 2 sets of frequencies. one set is (fs1,fs2) and the other set is (fp1,fp2)?

thanks

regards
scdoro

 

[Kral]

scdoro,
wu, wl refer tot the upper and lower passband corner frequencies. Regarding selection of a passband frequency to use for the low pass prototype, this is not so straightforward. Frequently the geometric mean between the upper and lower passband frequencies is used (Sqrt(wu X wl)). However, this results in an asymmetric response for both analog design and impulse invariant design. For the bilinear transform method, the problem is further complicated by the frequency warping. You have 3 choices:
~ Use wl for the low pass prototype, and take
~ what you get at the high end. This usually gives the
~ widest bandwidth.
~
~ Use wu for the low pass prototype, and take
~ what you get at the low end.
~
~ Use the geometric mean for the low pass prototype, and take
~ what you get at both the low end and the high end.
~
You will probably have to "cut and try" until you get acceptable results using the bilinear transform method, since you can only choose one frequency of the analog prototype at which to "pre-warp".
Regards,
Kral

 

[scdoro]

ok kral.

i think i got what you meant. Thanks. i have a hard time choosing what is a reasonable value for fp.Thats why want to consult you on that.

If i get the correct value for fp.Similarly,how do i get fs for the lowpass prototype filter?

regards
scdoro