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6.4.1 Challenge
March 29, 2016
3:06 am
Scoridd
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March 28, 2016
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Hi,

Can someone help me with the 6.4.1 challenge. I have been through it a number of times and corrected various mistakes I've made along the way but I've hit a dead end and can't see where I went wrong.

I assume my frequency pre-warping is OK as it is the same as in the previous example in the book:

Wa = tan[ WdT / 2 ] = 0.07136

Denormalize analogue transfer function:

0.005092
----------------------------------------
s^2 + 0.07136s + 0.005092

And BZT:

0.005092(z+1)^2
------------------------------------------------------------------
(z-1)^2 + 0.07136(z-1)(z+1) + 0.005092(z+1)^2

I think my error my be in the denormalize section but I can't see where. From what I've seen in other examples, the structure of the various powers of z seems right in the BZT but I may be mistaken. If anyone could offer any insight in to where I have gone wrong it would be very much appreciated!

March 29, 2016
3:30 am
W Pirkle
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January 29, 2017
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Hi

Well, the wording of the question is a bit confusing here and I apologize for that. It is slightly different from the way the previous problem is worded in that you are given a transfer function H(s) *with the analog LPF cutoff already calculated as 1kHz* so you do not need to find the pre-warped analog cutoff - you already have it. This was supposed to simplify the derivation but the wording caused issues. I've already fixed this for whenever the 2nd Edition is desired.

So, calculate the normalized wa as

wa = 2pifc/fs and then go from there.

You can find the solution here:

Sorry for any confusion with that wording.

Will

March 29, 2016
1:18 pm
Scoridd
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March 28, 2016
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OK gotcha, thanks for the speedy reply Will.

The book is great, I have been dipping in to Audio DSP for the last few years but banging my head against the wall trying to learn from the fragmented information in different papers/books, all with different terminology - so it's really useful to have it all in one resource.

I have the synthesiser book on order now too, I wrote a 303 emu a while ago but never really understood the filter, so I'm hoping this will help me crack that one.

March 30, 2016
1:14 am
Scoridd
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March 28, 2016
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Thanks for posting the solution Will. However, I found the solution has the frequency calculation listed incorrectly:

Wn = 2 PI Fc / Fs = 0.1425 (not 0.0714, as listed in the solution)

...it should be...

Wa = tan(WdT/2) = 0.0714

using the pre-warping calculation gives the correct value, which can then be used with the rest of the solution listed. Just wanted to mention it here for anyone else who might be looking.

As it turned out, I was on the right track - I just needed to multiply everything by z^-2 and then scale by the reciprocal of the non-z term in the denominator - sorted!

March 30, 2016
6:41 pm
W Pirkle
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Thanks!

I will update the solution file when I get a chance.

Will

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