Forums

Sampling, Again -- Updates

Started by Tim Wescott December 20, 2010
On 21 Dec., 00:19, Jerry Avins <j...@ieee.org> wrote:
> On Dec 20, 4:15&#2013266080;pm, Tim Wescott <t...@seemywebsite.com> wrote: > > > > > I'm starting a new thread (from "Sampling: What Nyquist Didn't Say, and > > What to Do About It"), because the old one rapidly filled up with all > > sorts of interesting stuff that I didn't want to detract from. > > > I've posted a new version. &#2013266080;It uses Bitstream fonts for Roman -- used > > because it was mentioned, and because it was there. &#2013266080;It's still a serif > > font which isn't optimum for monitor viewing, but I want the thing to > > look good when it's printed (and I'm lazy about figuring out how to tell > > Lyx/LaTeX how to use sans!). > > > It's 12-point, so you won't have to squint to see it, or have as much > > trouble scanning across the line. &#2013266080;It certainly looks better in Evince, > > and I'm about to find out how it looks in Adobe, on my wife's computer > > upstairs. > > > And Randy, I've changed the discussion of subsampling to make it more > > clear -- I hope that if it doesn't fully answer your difficulties (I > > think you thought I was claiming to sample at an effectively infinite > > rate) it does explain what I'm thinking more fully. > > > THANK YOU ALL who responded to the previous thread, and please don't > > feel shy if you see something that I still haven't caught! &#2013266080;I need to > > add an acknowledgements section for all the kind folks on USENET who > > critique my work. > > Please indulge a re-newbie question. Where is the paper under > discussion? > > Jerry
first one here I assume: http://www.wescottdesign.com/articles.html -Lasse
On Mon, 20 Dec 2010 15:34:55 -0800 (PST), "langwadt@fonz.dk"
<langwadt@fonz.dk> wrote:

>On 21 Dec., 00:19, Jerry Avins <j...@ieee.org> wrote: >> On Dec 20, 4:15=A0pm, Tim Wescott <t...@seemywebsite.com> wrote: >> >> >> >> > I'm starting a new thread (from "Sampling: What Nyquist Didn't Say, and >> > What to Do About It"), because the old one rapidly filled up with all >> > sorts of interesting stuff that I didn't want to detract from. >> >> > I've posted a new version. =A0It uses Bitstream fonts for Roman -- used >> > because it was mentioned, and because it was there. =A0It's still a ser= >if >> > font which isn't optimum for monitor viewing, but I want the thing to >> > look good when it's printed (and I'm lazy about figuring out how to tel= >l >> > Lyx/LaTeX how to use sans!). >> >> > It's 12-point, so you won't have to squint to see it, or have as much >> > trouble scanning across the line. =A0It certainly looks better in Evinc= >e, >> > and I'm about to find out how it looks in Adobe, on my wife's computer >> > upstairs. >> >> > And Randy, I've changed the discussion of subsampling to make it more >> > clear -- I hope that if it doesn't fully answer your difficulties (I >> > think you thought I was claiming to sample at an effectively infinite >> > rate) it does explain what I'm thinking more fully. >> >> > THANK YOU ALL who responded to the previous thread, and please don't >> > feel shy if you see something that I still haven't caught! =A0I need to >> > add an acknowledgements section for all the kind folks on USENET who >> > critique my work. >> >> Please indulge a re-newbie question. Where is the paper under >> discussion? >> >> Jerry > >first one here I assume: http://www.wescottdesign.com/articles.html > >-Lasse
1) Wow! Lasse is still around! Greetings! 2) Use the same link as from the previous thread: http://www.wescottdesign.com/articles/Sampling/sampling.pdf Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
On 12/20/2010 03:19 PM, Jerry Avins wrote:
> On Dec 20, 4:15 pm, Tim Wescott<t...@seemywebsite.com> wrote: >> I'm starting a new thread (from "Sampling: What Nyquist Didn't Say, and >> What to Do About It"), because the old one rapidly filled up with all >> sorts of interesting stuff that I didn't want to detract from. >> >> I've posted a new version. It uses Bitstream fonts for Roman -- used >> because it was mentioned, and because it was there. It's still a serif >> font which isn't optimum for monitor viewing, but I want the thing to >> look good when it's printed (and I'm lazy about figuring out how to tell >> Lyx/LaTeX how to use sans!). >> >> It's 12-point, so you won't have to squint to see it, or have as much >> trouble scanning across the line. It certainly looks better in Evince, >> and I'm about to find out how it looks in Adobe, on my wife's computer >> upstairs. >> >> And Randy, I've changed the discussion of subsampling to make it more >> clear -- I hope that if it doesn't fully answer your difficulties (I >> think you thought I was claiming to sample at an effectively infinite >> rate) it does explain what I'm thinking more fully. >> >> THANK YOU ALL who responded to the previous thread, and please don't >> feel shy if you see something that I still haven't caught! I need to >> add an acknowledgements section for all the kind folks on USENET who >> critique my work. > > Please indulge a re-newbie question. Where is the paper under > discussion?
Oi! Where's the emoticon for the forehead-slap? http://www.wescottdesign.com/articles/Sampling/sampling.pdf :-/ -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
On Dec 20, 6:19&#2013266080;pm, Jerry Avins <j...@ieee.org> wrote:


> Please indulge a re-newbie question. Where is the paper under > discussion?
Duh! I found it right away, but Google groups wouldn't let me respond for over an hour. Jerry
On Dec 21, 10:15&#2013266080;am, Tim Wescott <t...@seemywebsite.com> wrote:
> I'm starting a new thread (from "Sampling: What Nyquist Didn't Say, and > What to Do About It"), because the old one rapidly filled up with all > sorts of interesting stuff that I didn't want to detract from. > > I've posted a new version. &#2013266080;It uses Bitstream fonts for Roman -- used > because it was mentioned, and because it was there. &#2013266080;It's still a serif > font which isn't optimum for monitor viewing, but I want the thing to > look good when it's printed (and I'm lazy about figuring out how to tell > Lyx/LaTeX how to use sans!). > > It's 12-point, so you won't have to squint to see it, or have as much > trouble scanning across the line. &#2013266080;It certainly looks better in Evince, > and I'm about to find out how it looks in Adobe, on my wife's computer > upstairs. > > And Randy, I've changed the discussion of subsampling to make it more > clear -- I hope that if it doesn't fully answer your difficulties (I > think you thought I was claiming to sample at an effectively infinite > rate) it does explain what I'm thinking more fully. > > THANK YOU ALL who responded to the previous thread, and please don't > feel shy if you see something that I still haven't caught! &#2013266080;I need to > add an acknowledgements section for all the kind folks on USENET who > critique my work. > > -- > > Tim Wescott > Wescott Design Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html
What Nyquist didn't say: I vonder if they will noteece that I stole all zis crap from other authors like Whittacker and zat russian chappy..
On 12/20/2010 07:18 PM, HardySpicer wrote:
> On Dec 21, 10:15 am, Tim Wescott<t...@seemywebsite.com> wrote: >> I'm starting a new thread (from "Sampling: What Nyquist Didn't Say, and >> What to Do About It"), because the old one rapidly filled up with all >> sorts of interesting stuff that I didn't want to detract from. >> >> I've posted a new version. It uses Bitstream fonts for Roman -- used >> because it was mentioned, and because it was there. It's still a serif >> font which isn't optimum for monitor viewing, but I want the thing to >> look good when it's printed (and I'm lazy about figuring out how to tell >> Lyx/LaTeX how to use sans!). >> >> It's 12-point, so you won't have to squint to see it, or have as much >> trouble scanning across the line. It certainly looks better in Evince, >> and I'm about to find out how it looks in Adobe, on my wife's computer >> upstairs. >> >> And Randy, I've changed the discussion of subsampling to make it more >> clear -- I hope that if it doesn't fully answer your difficulties (I >> think you thought I was claiming to sample at an effectively infinite >> rate) it does explain what I'm thinking more fully. >> >> THANK YOU ALL who responded to the previous thread, and please don't >> feel shy if you see something that I still haven't caught! I need to >> add an acknowledgements section for all the kind folks on USENET who >> critique my work. >> >> -- >> >> Tim Wescott >> Wescott Design Serviceshttp://www.wescottdesign.com >> >> Do you need to implement control loops in software? >> "Applied Control Theory for Embedded Systems" was written for you. >> See details athttp://www.wescottdesign.com/actfes/actfes.html > > What Nyquist didn't say: I vonder if they will noteece that I stole > all zis crap from other authors like Whittacker and zat russian > chappy.. >
Actually, as near as I can tell without meticulously going through a bunch of papers from the late 40's, the use of the Nyquist rate as a limit on PCM modulation was articulated by Shannon, who was just very precise about crediting Nyquist with being _his_ source of information. I think that the various sampling theorems must have arisen from the zeitgeist of the early 20th century -- everyone was working on similar problems, and were using similar mathematical tools, so they all arrived at similar results at (roughly) similar times. Even though the 'similar' times were spread out by years, the barriers of language, commercial interests, and separate sub-disciplines means that the results were still arrived at independently (probably). -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
On Dec 22, 6:30&#2013266080;am, Tim Wescott <t...@seemywebsite.com> wrote:
> On 12/20/2010 07:18 PM, HardySpicer wrote: > > > On Dec 21, 10:15 am, Tim Wescott<t...@seemywebsite.com> &#2013266080;wrote: > >> I'm starting a new thread (from "Sampling: What Nyquist Didn't Say, and > >> What to Do About It"), because the old one rapidly filled up with all > >> sorts of interesting stuff that I didn't want to detract from. > > >> I've posted a new version. &#2013266080;It uses Bitstream fonts for Roman -- used > >> because it was mentioned, and because it was there. &#2013266080;It's still a serif > >> font which isn't optimum for monitor viewing, but I want the thing to > >> look good when it's printed (and I'm lazy about figuring out how to tell > >> Lyx/LaTeX how to use sans!). > > >> It's 12-point, so you won't have to squint to see it, or have as much > >> trouble scanning across the line. &#2013266080;It certainly looks better in Evince, > >> and I'm about to find out how it looks in Adobe, on my wife's computer > >> upstairs. > > >> And Randy, I've changed the discussion of subsampling to make it more > >> clear -- I hope that if it doesn't fully answer your difficulties (I > >> think you thought I was claiming to sample at an effectively infinite > >> rate) it does explain what I'm thinking more fully. > > >> THANK YOU ALL who responded to the previous thread, and please don't > >> feel shy if you see something that I still haven't caught! &#2013266080;I need to > >> add an acknowledgements section for all the kind folks on USENET who > >> critique my work. > > >> -- > > >> Tim Wescott > >> Wescott Design Serviceshttp://www.wescottdesign.com > > >> Do you need to implement control loops in software? > >> "Applied Control Theory for Embedded Systems" was written for you. > >> See details athttp://www.wescottdesign.com/actfes/actfes.html > > > What Nyquist didn't say: I vonder if they will noteece that I stole > > all zis crap from other authors like Whittacker and zat russian > > chappy.. > > Actually, as near as I can tell without meticulously going through a > bunch of papers from the late 40's, the use of the Nyquist rate as a > limit on PCM modulation was articulated by Shannon, who was just very > precise about crediting Nyquist with being _his_ source of information. > > I think that the various sampling theorems must have arisen from the > zeitgeist of the early 20th century -- everyone was working on similar > problems, and were using similar mathematical tools, so they all arrived > at similar results at (roughly) similar times. &#2013266080;Even though the > 'similar' times were spread out by years, the barriers of language, > commercial interests, and separate sub-disciplines means that the > results were still arrived at independently (probably). > > -- > > Tim Wescott > Wescott Design Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html
http://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_formula
On 21/12/2010 8:15 AM, Tim Wescott wrote:
> I'm starting a new thread (from "Sampling: What Nyquist > Didn't Say, and What to Do About It"), because the old one > rapidly filled up with all sorts of interesting stuff that I > didn't want to detract from. > > I've posted a new version. It uses Bitstream fonts for Roman > -- used because it was mentioned, and because it was there. > It's still a serif font which isn't optimum for monitor > viewing, but I want the thing to look good when it's printed > (and I'm lazy about figuring out how to tell Lyx/LaTeX how > to use sans!). > > It's 12-point, so you won't have to squint to see it, or > have as much trouble scanning across the line. It certainly > looks better in Evince, and I'm about to find out how it > looks in Adobe, on my wife's computer upstairs. > > And Randy, I've changed the discussion of subsampling to > make it more clear -- I hope that if it doesn't fully answer > your difficulties (I think you thought I was claiming to > sample at an effectively infinite rate) it does explain what > I'm thinking more fully. > > THANK YOU ALL who responded to the previous thread, and > please don't feel shy if you see something that I still > haven't caught! I need to add an acknowledgements section > for all the kind folks on USENET who critique my work. >
Tim, Thanks for making available a clear and informative paper. I would like to make a comment at this late stage about the section on signal reconstruction, mainly about terminology. You explain that reconstruction is done by interpolating the output signal but unfortunately I feel that you have not clearly identified where the interpolaton occurs. You say that the first step in interpolation is the generation of a stepped waveform by the zero-hold D/A and you mention the stepped waveform of Figure 5 as being a picture of an interpolated signal. In my view this should be changed to say that generating the stepped waveform is the first step in the reconstruction process, interpolaton being the second step. Interpolation, the generation of intermediate values between known data points, occurs when the stepped analog signal reaches the analog output reconstruction filter. It is the analog components that generate the intermediate data values, on a continuous basis. You have mentioned the output filter, and I think it would be useful to identify this filter as the spot where interpolation occurs. Regards, John
On Wed, 22 Dec 2010 11:10:41 +1100, John Monro
<johnmonro@optusnet.com.au> wrote:

>On 21/12/2010 8:15 AM, Tim Wescott wrote: >> I'm starting a new thread (from "Sampling: What Nyquist >> Didn't Say, and What to Do About It"), because the old one >> rapidly filled up with all sorts of interesting stuff that I >> didn't want to detract from. >> >> I've posted a new version. It uses Bitstream fonts for Roman >> -- used because it was mentioned, and because it was there. >> It's still a serif font which isn't optimum for monitor >> viewing, but I want the thing to look good when it's printed >> (and I'm lazy about figuring out how to tell Lyx/LaTeX how >> to use sans!). >> >> It's 12-point, so you won't have to squint to see it, or >> have as much trouble scanning across the line. It certainly >> looks better in Evince, and I'm about to find out how it >> looks in Adobe, on my wife's computer upstairs. >> >> And Randy, I've changed the discussion of subsampling to >> make it more clear -- I hope that if it doesn't fully answer >> your difficulties (I think you thought I was claiming to >> sample at an effectively infinite rate) it does explain what >> I'm thinking more fully. >> >> THANK YOU ALL who responded to the previous thread, and >> please don't feel shy if you see something that I still >> haven't caught! I need to add an acknowledgements section >> for all the kind folks on USENET who critique my work. >> > >Tim, >Thanks for making available a clear and informative paper. I >would like to make a comment at this late stage about the >section on signal reconstruction, mainly about terminology. > >You explain that reconstruction is done by interpolating the >output signal but unfortunately I feel that you have not >clearly identified where the interpolaton occurs. > >You say that the first step in interpolation is the >generation of a stepped waveform by the zero-hold D/A and >you mention the stepped waveform of Figure 5 as being a >picture of an interpolated signal. In my view this should be >changed to say that generating the stepped waveform is the >first step in the reconstruction process, interpolaton being >the second step.
The ideal reconstruction is an impulse generator (not the ZOH) followed by an ideal lowpass filter. That avoids the sinc frequency error thingie you get from the ZOH. John
On 12/21/2010 04:10 PM, John Monro wrote:
> On 21/12/2010 8:15 AM, Tim Wescott wrote: >> I'm starting a new thread (from "Sampling: What Nyquist >> Didn't Say, and What to Do About It"), because the old one >> rapidly filled up with all sorts of interesting stuff that I >> didn't want to detract from. >> >> I've posted a new version. It uses Bitstream fonts for Roman >> -- used because it was mentioned, and because it was there. >> It's still a serif font which isn't optimum for monitor >> viewing, but I want the thing to look good when it's printed >> (and I'm lazy about figuring out how to tell Lyx/LaTeX how >> to use sans!). >> >> It's 12-point, so you won't have to squint to see it, or >> have as much trouble scanning across the line. It certainly >> looks better in Evince, and I'm about to find out how it >> looks in Adobe, on my wife's computer upstairs. >> >> And Randy, I've changed the discussion of subsampling to >> make it more clear -- I hope that if it doesn't fully answer >> your difficulties (I think you thought I was claiming to >> sample at an effectively infinite rate) it does explain what >> I'm thinking more fully. >> >> THANK YOU ALL who responded to the previous thread, and >> please don't feel shy if you see something that I still >> haven't caught! I need to add an acknowledgements section >> for all the kind folks on USENET who critique my work. >> > > Tim, > Thanks for making available a clear and informative paper. I would like > to make a comment at this late stage about the section on signal > reconstruction, mainly about terminology. > > You explain that reconstruction is done by interpolating the output > signal but unfortunately I feel that you have not clearly identified > where the interpolaton occurs. > > You say that the first step in interpolation is the generation of a > stepped waveform by the zero-hold D/A and you mention the stepped > waveform of Figure 5 as being a picture of an interpolated signal. In my > view this should be changed to say that generating the stepped waveform > is the first step in the reconstruction process, interpolaton being the > second step. > > Interpolation, the generation of intermediate values between known data > points, occurs when the stepped analog signal reaches the analog output > reconstruction filter. It is the analog components that generate the > intermediate data values, on a continuous basis. You have mentioned the > output filter, and I think it would be useful to identify this filter as > the spot where interpolation occurs.
I thought about that before I used the term, and I like my way. The reason I used it is because, in the context of that paper (and as I generally think about sampling), the sampled time signal _does not exist_ in between the sampling instants. That's a rather strict way to consider things, but I find it keeps me from miss-applying continuous-time wisdom to sampled time systems. Since the signal _doesn't_ exist, the action of a ZOH is, indeed, to interpolate. The usage is different from what some people would use, but I (a) don't think it's all that far off, (b) think it's more accurate, and (c) think that if someone can't handle Author A using different terminology from Author B, then they can't handle engineering. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html