Looking for a GOOD explanation of the proof and application of DST, and other DSP techniques.. DSP encyclopedia?

I was reading some tutorials @ dspdimension.com, and they were talking
about techniques that I'd never heard of before, such as the Discrete Sine
Transform.  The explanation was understandable if the reader does a lot of
thinking, but more diagrams and possibly even animations would convey the
concepts more clearly and require much less time from the reader. 
(Although to be fair, it seems like almost no authors of technical material
go to these lengths.. kind of a shame I think.. I think it was Feynman who
said something like "For anything we really understand, we should be able
to craft an explanation that even a child can understand.")
Explaining the proof would probably clear up any lingering
doubts/undiscussed logical holes in the readers mind, provided that the
proof is presented in a clear manner accompanied by plenty of diagrams
and/or animations.. but this is outside the scope of the tutorial.


This got me thinking: I have no formal education in DSP, and recently I've
been stumbling across all sorts of techniques that I previously didn't know
existed, many of which have potential to be very useful for what I'm
interested in.  Since I don't have the luxury (or torture, depending on how
you look at it =P ) of a formalized education in DSP, can anyone recommend
book(s)/website(s) that present a complete list and explanation of the full
library of DSP techniques, or do a very good job of explaining at least one
DSP technique?

I read Lyons' "Understanding Digital Signal Processing," I thought it did
a very good job of explaining the material that it covered.. but it seems
like there is so much out there that it didn't cover.  It didn't get into
proofs either, which would have been nice but is just outside the scope of
the book.

My interest is entirely in Spectral modeling of audio signals, and only in
audio timestretching as it may be useful in Spectral analysis (stretch the
signal to provide a longer signal for the FT to analyze in order to
increase FT resolution, then multiply resynthesis playback speed by the
inverse of the stretch amount in order to get back to original signal's
playback speed, something like that), and any techniques that may prove
useful in these regards (could be anything really, u never know..)


Any other advice/input would be much appreciated too..

Thank you

"maxplanck" <erik.bowen@comcast.net> wrote in 
news:Bc6dnSMJB_Gge6PVnZ2dnUVZ_sudnZ2d@giganews.com:

> I was reading some tutorials @ dspdimension.com, and they were talking
> about techniques that I'd never heard of before, such as the Discrete 
Sine
> Transform.  The explanation was understandable if the reader does a lot 
of
> thinking, but more diagrams and possibly even animations would convey the
> concepts more clearly and require much less time from the reader. 
> (Although to be fair, it seems like almost no authors of technical 
material
> go to these lengths.. kind of a shame I think.. I think it was Feynman 
who
> said something like "For anything we really understand, we should be able
> to craft an explanation that even a child can understand.")
> Explaining the proof would probably clear up any lingering
> doubts/undiscussed logical holes in the readers mind, provided that the
> proof is presented in a clear manner accompanied by plenty of diagrams
> and/or animations.. but this is outside the scope of the tutorial.
> 
> 
> This got me thinking: I have no formal education in DSP, and recently 
I've
> been stumbling across all sorts of techniques that I previously didn't 
know
> existed, many of which have potential to be very useful for what I'm
> interested in.  Since I don't have the luxury (or torture, depending on 
how
> you look at it =P ) of a formalized education in DSP, can anyone 
recommend
> book(s)/website(s) that present a complete list and explanation of the 
full
> library of DSP techniques, or do a very good job of explaining at least 
one
> DSP technique?

I have maybe 50 DSP books and collectively they do not constitute "The book 
of everything". 

Most of us have been doing this for many years and most of us have a 
formalized engineering or scientifc education including the math 
foundation. I would like to think that everything we know couldn't be 
summarized in just one book.

That said, I think that you can learn a lot about DSP by doing some of the 
things you are doing, but it will take effort on your part (pain or 
luxury). Even the most talented musicians or athletes practice, practice 
practice.


> 
> I read Lyons' "Understanding Digital Signal Processing," I thought it did
> a very good job of explaining the material that it covered.. but it seems
> like there is so much out there that it didn't cover.  It didn't get into
> proofs either, which would have been nice but is just outside the scope 
of
> the book.

One of the best choices. Steven Smith's book is another. We have posted 
favorites from time to time in this group. I would Google.



Al Clark
Danville Signal Processing, Inc.

maxplanck wrote:

>        ... can anyone recommend
> book(s)/website(s) that present a complete list and explanation of the full
> library of DSP techniques, or do a very good job of explaining at least one
> DSP technique?

Get real. A complete list today will be incomplete by evening.

> I read Lyons' "Understanding Digital Signal Processing," I thought it did
> a very good job of explaining the material that it covered.. but it seems
> like there is so much out there that it didn't cover.  It didn't get into
> proofs either, which would have been nice but is just outside the scope of
> the book.
> 
> My interest is entirely in Spectral modeling of audio signals, and only in
> audio timestretching as it may be useful in Spectral analysis (stretch the
> signal to provide a longer signal for the FT to analyze in order to
> increase FT resolution, then multiply resynthesis playback speed by the
> inverse of the stretch amount in order to get back to original signal's
> playback speed, something like that), and any techniques that may prove
> useful in these regards (could be anything really, u never know..)

A forlorn hope, I'm afraid. (As the sailor said, "A frayed knot.") All 
the relevant information is in the original data. Stretching the time 
base may give your brain time to keep up with your ears, but it can do 
nothing for an analysis algorithm.

> Any other advice/input would be much appreciated too..

Check out the bibliographies at http://www.dspguru.com. If it's not on 
the list, check out http://www.bores.com (lower right corner) also.

> Thank you

You're welcome, Max.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

I'm checking out Steven Smith's book, looks like I can learn some more
here.  I will search the sites you recommended and this forum for more book
recommendations, thanks!


The FT of 50000 cycles of a sine wave is much clearer than the FT of one
cycle of a sine wave, no?  This is the logic that led me to think that
timestretching a signal may improve FT results, would you mind explaining a
bit more about why this won't work Jerry?

On May 29, 3:17 pm, "maxplanck" <erik.bo...@comcast.net> wrote:
> I'm checking out Steven Smith's book, looks like I can learn some more
> here.  I will search the sites you recommended and this forum for more book
> recommendations, thanks!
>
> The FT of 50000 cycles of a sine wave is much clearer than the FT of one
> cycle of a sine wave, no?  This is the logic that led me to think that
> timestretching a signal may improve FT results, would you mind explaining a
> bit more about why this won't work Jerry?

Time stretching doesn't add new information, it just duplicates
existing information.  50 copies of the first page of a book
is usually far less informative than 50 non-duplicated pages.

What looks cleaner from your FT might just be an artifact of
the  assumptions you made in creating 49999 duplicate cycles
from the 1 cycle of actual information.

.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
 http://www.nicholson.com/rhn/dsp.html

>Time stretching doesn't add new information, it just duplicates
>existing information.  50 copies of the first page of a book
>is usually far less informative than 50 non-duplicated pages.
>
>What looks cleaner from your FT might just be an artifact of
>the  assumptions you made in creating 49999 duplicate cycles
>from the 1 cycle of actual information.
>
>.
>
>
>IMHO. YMMV.
>--
>rhn A.T nicholson d.0.t C-o-M
> http://www.nicholson.com/rhn/dsp.html


Isn't it a basic property of the FT that for a given periodic signal, with
increased signal length comes increased resolution in the FT's output?

maxplanck wrote:
> I'm checking out Steven Smith's book, looks like I can learn some more
> here.  I will search the sites you recommended and this forum for more book
> recommendations, thanks!
> 
> 
> The FT of 50000 cycles of a sine wave is much clearer than the FT of one
> cycle of a sine wave, no?  This is the logic that led me to think that
> timestretching a signal may improve FT results, would you mind explaining a
> bit more about why this won't work Jerry?

The more you stretch the signal, the more you degrade it. That's really 
beside the point, though. Whatever stretched signal you make, it can 
have no more information than went into the stretcher. If by some 
miracle the stretched signal is not degraded, then you have all the 
original information but no more. So you can lose, but you can't win.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

maxplanck wrote:
>> Time stretching doesn't add new information, it just duplicates
>> existing information.  50 copies of the first page of a book
>> is usually far less informative than 50 non-duplicated pages.
>>
>> What looks cleaner from your FT might just be an artifact of
>> the  assumptions you made in creating 49999 duplicate cycles
>>from the 1 cycle of actual information.
>> .
>>
>>
>> IMHO. YMMV.
>> --
>> rhn A.T nicholson d.0.t C-o-M
>> http://www.nicholson.com/rhn/dsp.html
> 
> 
> Isn't it a basic property of the FT that for a given periodic signal, with
> increased signal length comes increased resolution in the FT's output?

 From those 5000 "clean" cycles, you can very accurately determine the 
frequency. It will turn out to be *exactly* the frequency you assumed 
when you arbitrarily selected the single segment to duplicate.

The beauty of this method is that it always confirms your initial guess, 
no matter how far off it is. That is explaining today's clear sky and 
yesterday's rain as the will of God. Ehat explains everything explains 
nothing.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

> From those 5000 "clean" cycles, you can very accurately determine the 
>frequency. It will turn out to be *exactly* the frequency you assumed 
>when you arbitrarily selected the single segment to duplicate.

Isn't the goal to determine what combination of sine waves will most
closely reproduce the original signal?  If so, doesn't this meet that
criteria, at least for this particular segment of the signal?


I've tried looping the region between every other zero crossing of an
audio signal (loop starts @ zero crossing, positive portion, zero crossing,
negative portion, loop ends @ zero crossing) and then running an FT on that
loop, and the resulting spectrum is way different from the spectrum I get
for that region when I run the whole signal through a STFT analyzer such as
SPEAR, so I can see from this that looping regions is not useful.  

I suppose I should read more about the STFT, that would probably clear up
why looping individual regions is useless.

On May 30, 1:22 am, "maxplanck" <erik.bo...@comcast.net> wrote:

> I read Lyons' "Understanding Digital Signal Processing," I thought it did
> a very good job of explaining the material that it covered.. but it seems
> like there is so much out there that it didn't cover.  It didn't get into
> proofs either, which would have been nice but is just outside the scope of
> the book.

I've seen estimates that there are about 50,000 DSP engineers in the
world. I have no idea how those estimates are arrived at, or what they
class as a DSP engineer - Someone who touches a little DSP from time
to time? Someone who programs the stuff all day, but has a weak
understanding of the principals? Someone who cooks up the deepest of
algorithms for fun and profit? Anyway, its not a huge number, but its
enough that they are working is a heck of a lot of application areas.

I finally got a copy of Rick Lyons book recently. Since the local
retail price is RMB59 (about US$8), it didn't add much to the bill
when I noticed it while buying something else. :-) People have been
recommending this book heavily for ages, and now I see why. I think it
strikes an excellent balance for an introductory text. If it included
the proofs of everything it covers, it would get bogged down in no
time. If it tried to focus on a lot of application specifics, it would
get bogged down even faster. I think its a great first book. It is a
first book, though. Most signal processing books are considerably
thicker, while covering one narrow subject matter, and leaving out
most of the juicy details that lead to successful applications. :-)
Its interesting how even the thickest signal processing books, on the
narrowest of topics, are still only able to skim over the subject
matter. Our job must be HUGE! :-)

Regards,
Steve