Reply by axlq August 12, 20042004-08-12
In article <10hnmhe7on11jd1@corp.supernews.com>,
Tim Wescott  <tim@wescottnospamdesign.com> wrote:
>>>ftp://ftp.deltacompsys.com/public/mcd/Bessel%20High%20Pass.htm >> transfer function is s^2 / (s^2 + 3s + 3). >> >> Here's a page full of Bessel filter constants: >> http://www.crbond.com/papers/bsf.pdf >> transfer function is 3 / (s^2 + 3s + 3). >> >> How are the two reconciled? > >The first one is a high-pass filter, the second is low-pass.
Well yes, but I thought one can convert one to the other, say by H(highpass) = 1 - H(lowpass). I also thought maybe that by substituting 1/s in the transfer function one switches from lowpass to highpass. Either way, I can't reconcile them.
>See my article at >http://www.wescottdesign.com/articles/zTransform/z-transforms.html >for a development of the concept of "transfer function" -- it's all >in the z domain, but the concept applies to the s domain as well.
Thanks, I've bookmarked it and I'm studying it now. -Alex
Reply by Tim Wescott August 12, 20042004-08-12
axlq wrote:

> [posted and emailed] > > Peter, I apologize for reviving this part of a past discussion, but > there's a point I'm not clear on, and it has mostly to do with my > ignorance about where to start from when constructing a filter. > > In article <XvydnQv1cPdCKZDcRVn-qg@comcast.com>, > Peter Nachtwey <peter@deltacompsys.com> wrote: > > >>ftp://ftp.deltacompsys.com/public/mcd/Bessel%20High%20Pass.htm >>A high pass Bessel filter. It doesn't look much different from >>the Butterworth filter. Beware, the corner frequencies are really >>higher than the value used in the calculations. The filters aren't >>hard to make if you have Mathcad. > > > Your normalized Bessel function (is this what's also called the > "transfer function"?), about halfway down your page, is > s^2 / (s^2 + 3s + 3). > > Here's a page full of Bessel filter constants: > http://www.crbond.com/papers/bsf.pdf > > ...which shows (equation 6) the transfer function as > 3 / (s^2 + 3s + 3). > > How are the two reconciled? Your page describes clearly the steps > in constructing a filter (assuming I have something like MathCad > available), but it seems to start from a different filter function > than what I can find published elsewhere for Bessel filters. > > Thanks. > -Alex > > [posted and emailed - not sure if you're still following comp.dsp]
The first one is a high-pass filter, the second is low-pass. See my article at http://www.wescottdesign.com/articles/zTransform/z-transforms.html for a development of the concept of "transfer function" -- it's all in the z domain, but the concept applies to the s domain as well. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by axlq August 12, 20042004-08-12
[posted and emailed]

Peter, I apologize for reviving this part of a past discussion, but
there's a point I'm not clear on, and it has mostly to do with my
ignorance about where to start from when constructing a filter.

In article <XvydnQv1cPdCKZDcRVn-qg@comcast.com>,
Peter Nachtwey <peter@deltacompsys.com> wrote:

>ftp://ftp.deltacompsys.com/public/mcd/Bessel%20High%20Pass.htm >A high pass Bessel filter. It doesn't look much different from >the Butterworth filter. Beware, the corner frequencies are really >higher than the value used in the calculations. The filters aren't >hard to make if you have Mathcad.
Your normalized Bessel function (is this what's also called the "transfer function"?), about halfway down your page, is s^2 / (s^2 + 3s + 3). Here's a page full of Bessel filter constants: http://www.crbond.com/papers/bsf.pdf ...which shows (equation 6) the transfer function as 3 / (s^2 + 3s + 3). How are the two reconciled? Your page describes clearly the steps in constructing a filter (assuming I have something like MathCad available), but it seems to start from a different filter function than what I can find published elsewhere for Bessel filters. Thanks. -Alex [posted and emailed - not sure if you're still following comp.dsp]
Reply by glen herrmannsfeldt August 8, 20042004-08-08
Jerry Avins wrote:

> This excerpt explains a little of how he came to be Lord Kelvin. > http://www.wordiq.com/definition/William_Thomson,_1st_Baron_Kelvin
(snip)
> The merit of this receiving instrument is, that > it indicates with extreme sensibility all the variations of the current > in the cable, so that, instead of having to wait until each signal wave > sent into the cable has travelled to the receiving end before sending > another, a series of waves may be sent after each other in rapid > succession. These waves, encroaching upon each other, will coalesce at > their bases; but if the crests remain separate, the delicate decipherer > at the other end will take cognisance of them and make them known to the > eye as the distinct signals of the message. > Mirror galvanometer
(snip) And note that Nyquist was not working one sampling of analog signals, but on how fast pulses could be sent down a cable with a limited bandwidth. Different problems with the same solution. -- glen
Reply by Jerry Avins August 7, 20042004-08-07
axlq wrote:

> In article <41144572$0$5908$61fed72c@news.rcn.com>, > Jerry Avins <jya@ieee.org> wrote: > >>But as Alex correctly pointed out, the response of a 1st-order analog >>high pass to a step is 1 - exp(-t/T), which has monotonic decay without >>undershoot. That single counterexample disproves my argument. > > > Not really -- your argument holds for a filter order higher than > 1. My empirical tests indicate that the number of zero-crossings of > a critically-damped high-pass filter is proportional to the order, > as n-1 crossings for order n. If there's no way to "fix" that > situation, then I have to live with it. > > -Alex
The conclusion is probably true, but the "proof" itself is invalid. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Reply by axlq August 7, 20042004-08-07
In article <41144572$0$5908$61fed72c@news.rcn.com>,
Jerry Avins  <jya@ieee.org> wrote:
>But as Alex correctly pointed out, the response of a 1st-order analog >high pass to a step is 1 - exp(-t/T), which has monotonic decay without >undershoot. That single counterexample disproves my argument.
Not really -- your argument holds for a filter order higher than 1. My empirical tests indicate that the number of zero-crossings of a critically-damped high-pass filter is proportional to the order, as n-1 crossings for order n. If there's no way to "fix" that situation, then I have to live with it. -Alex
Reply by Jerry Avins August 6, 20042004-08-06
Jon Harris wrote:
> "axlq" <axlq@spamcop.net> wrote in message news:cf0in5$iif$1@blue.rahul.net...
...
>>My expectation of a HP critically damped step response is that the >>filter output immediately jumps, then approaches zero as rapidly as >>possible without dipping below. > > > As far as I know, this isn't possible. Jerry outlined a proof in another post.
But as Alex correctly pointed out, the response of a 1st-order analog high pass to a step is 1 - exp(-t/T), which has monotonic decay without undershoot. That single counterexample disproves my argument. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Reply by axlq August 6, 20042004-08-06
In article <2nhtgcF14t3fU1@uni-berlin.de>,
Jon Harris <goldentully@hotmail.com> wrote:
>> > On my page http://unicorn.us.com/alex/buttercrit.html is there >> > a way to get Q from the information there? Or do I need a >> > different approach? > >I took another look, Q is related to your damping d. So you should >just be able to pick any value of d you like to get a smoother time >response (and the corresponding less sharp frequency response).
I tried that. It shifts the cutoff frequency, and when I adjust the cutoff to shift it back, I end up with something that looks like a 2nd-order filter again, at least in the time domain -- I haven't checked the frequency response yet.
>> I haven't looked at your page, but try >> http://www.harmony-central.com/Computer/Programming/Audio-EQ-Cook >> book.txt. There are simple equations for the biquad coefs given >> cutoff frequency and Q. Pick any value of Q you like to obtain >> the desired time-domain response.
Thanks! I think you or someone else posted that link before in this thread, and I have it bookmarked. -Alex
Reply by axlq August 6, 20042004-08-06
In article <xxpsmb0116p.fsf@usrts005.corpusers.net>,
Randy Yates  <randy.yates@sonyericsson.com> wrote:
>> H(s) = S^2 / (S^2 + 3S + 3) where S = s/omega >> >> Opening my Schaum's Mathematical Handbook and turning to the chapter >> on Bessel functions, I can find nothing that looks like the function >> above. > >All I can say is, don't feel bad. The relationship between the two seems >to come from something called "umbral calculus." This document seems >to describe it well (not that I've read the entire thing) > > http://www.combinatorics.org/Surveys/ds3.pdf
Ugh. I thought there was a simple answer. Thanks for the info. -Alex
Reply by axlq August 6, 20042004-08-06
In article <4113d391$0$5922$61fed72c@news.rcn.com>,
Jerry Avins  <jya@ieee.org> wrote:
> Proof that All High-Pass Filters Ring when Presented with Step Inputs > &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295; >1) DC can't get through a high-pass filter, so the integral of its > response to any signal must be zero. >2) The rising edge of a step input is all high frequency. It passes > the filter unchanged in sign and magnitude (scaling excepted). >3) In order that the integral of a curve be zero, it must have as much > negative area as positive. Therefore, a high-pass-filiered positive > step must have both positive and negative regions. That's ringing. > >Does the argument break down?
Only in the case of a 1st order filter, which doesn't ring at all. But based on this, and other messages you and others have posted, I'm convinced that what I seek is a futile search, unless there's some trick to combine filters to cancel out the ringing. I could do this with low-pass filters, but never managed with a high pass filter. -Alex