Sampling, Again -- Updates

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 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

In comp.dsp Tim Wescott <tim@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.

(snip)

I do wonder how many people who discuss Nyquist have ever actually
read his paper.  I used to have a copy of it.  It isn't hard to
find in most university libraries, (at least ones old enough to
have been around).

-- glen

On 12/20/2010 01:30 PM, glen herrmannsfeldt wrote:
> In comp.dsp Tim Wescott<tim@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.
>
> (snip)
>
> I do wonder how many people who discuss Nyquist have ever actually
> read his paper.  I used to have a copy of it.  It isn't hard to
> find in most university libraries, (at least ones old enough to
> have been around).
>
> -- glen

The title is actually a bit of a misnomer, in that it's really the 
Nyquist-Shannon theorem, and if you get some continental input there's a 
Russian guy who figured out the same stuff.

It was motivated by a bunch of folks who all came onto comp.dsp, 
comp.arch.embedded, and sci.electronics.design and said "Nyquist says" 
followed by something naive and incorrect.  I actually replied to a few 
posts with "Nyquist _didn't_ say that" before I realized that I had a 
title and paper concept staring me in the face.

-- 

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 12/20/2010 10:30 PM, glen herrmannsfeldt wrote:
> In comp.dsp Tim Wescott <tim@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.
> 
> (snip)
> 
> I do wonder how many people who discuss Nyquist have ever actually
> read his paper.  I used to have a copy of it.  It isn't hard to
> find in most university libraries, (at least ones old enough to
> have been around).

Anyway, he only sort-of states his criterion, without proof. It was
Claude Shannon who actually gave a -remarkably short- demonstration
in his 1949 paper "Communication in the presence of noise".

Neither were first, by any means. For example, V. Kotelnikov stated
basically the same thing, much more verbosely, in the context of
interpolation theory. And before that, in 1915, E.T Whittaker wrote
something similar, and before that there was this Japanese fellow...
You get the idea.

Jeroen Belleman

On 12/20/2010 04:15 PM, Tim Wescott wrote:
> [...]
> 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,

Appearance-wise this looks EXCELLENT to my eyes! The fonts are now
vector, at least all the ones I checked.

FYI, a nice sans font I like to use is palatino. Simply place \usepackage{palatino}
near the top, e.g.:

\documentclass[english,11pt]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{palatino}

I'm reading the content now...
-- 
Randy Yates                      % "My Shangri-la has gone away, fading like
Digital Signal Labs              %  the Beatles on 'Hey Jude'"
yates@digitalsignallabs.com      %
http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO

On 12/20/2010 02:34 PM, Randy Yates wrote:
> On 12/20/2010 04:15 PM, Tim Wescott wrote:
>> [...]
>> 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,
>
> Appearance-wise this looks EXCELLENT to my eyes! The fonts are now
> vector, at least all the ones I checked.
>
> FYI, a nice sans font I like to use is palatino. Simply place
> \usepackage{palatino}
> near the top, e.g.:
>
> \documentclass[english,11pt]{article}
> \usepackage[T1]{fontenc}
> \usepackage[utf8]{inputenc}
> \usepackage{babel}
> \usepackage{palatino}
>
> I'm reading the content now...

I think that for the moment I'm going to register any comments, and 
unless someone comes up with something really tremendously bad, I'm 
going to move on to all the _other_ grotty papers I have that need to be 
improved.  They're all old OpenOffice documents that have been printed 
out as HTML, with all sorts of problems.

So -- I'd rather have a bunch of pretty good documents than one really 
excellent one.

I'm trying to decide if I want to do a paper next, or if I want to start 
in on all the homework problems I did for the first 1/2 of "Applied 
Control Theory for Embedded Systems".

-- 

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 12/20/2010 05:34 PM, Randy Yates wrote:
> [...]
> FYI, a nice sans font I like to use is palatino.

I made a comedy of errors with that statement! Palatino is serif, not
sans serif! Also, the psnfss document (texdoc psnfss), which is itself
some six years old, states that palatino is obsolete and instead
suggests to use mathpazo.

Sorry!
-- 
Randy Yates                      % "My Shangri-la has gone away, fading like
Digital Signal Labs              %  the Beatles on 'Hey Jude'"
yates@digitalsignallabs.com      %
http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO

On Mon, 20 Dec 2010 13:15:04 -0800, Tim Wescott <tim@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.

Looks great with Foxit.

John

On Dec 20, 4:15&#4294967295;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. &#4294967295;It uses Bitstream fonts for Roman -- used
> because it was mentioned, and because it was there. &#4294967295;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. &#4294967295;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! &#4294967295;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

In comp.dsp Tim Wescott <tim@seemywebsite.com> wrote:

(snip)

>> I do wonder how many people who discuss Nyquist have ever actually
>> read his paper.  I used to have a copy of it.  It isn't hard to
>> find in most university libraries, (at least ones old enough to
>> have been around).
 
> The title is actually a bit of a misnomer, in that it's really the 
> Nyquist-Shannon theorem, and if you get some continental input there's a 
> Russian guy who figured out the same stuff.

Still, it is interesting to read the older papers and see how
they thought about things differently, or not so much differently,
than we do today.

It also reminds me of the introduction to an ISDN book explaining
the first time that the electronic communications system was
all digital.  Nyquist was trying to get digital signals through
an analog channel, now we put (digitized) analog signals through 
a digital channel.  Same math, though.
 
> It was motivated by a bunch of folks who all came onto comp.dsp, 
> comp.arch.embedded, and sci.electronics.design and said "Nyquist says" 
> followed by something naive and incorrect.  I actually replied to a few 
> posts with "Nyquist _didn't_ say that" before I realized that I had a 
> title and paper concept staring me in the face.

-- glen