On Sunday, December 15, 2019 at 8:31:26 PM UTC-8, Richard (Rick) Lyons wrote:
> On Sunday, December 15, 2019 at 1:20:36 AM UTC-8, Christian Gollwitzer wrote:
> > Am 15.12.19 um 03:44 schrieb hdre..@freenet.de:
> > The FFT assumes that the input signal is periodic and
> > repeats infinitely many times.
> The unfortunately popular notion that "The FFT assumes its input
> is periodic" must surely be the most profound misconception
> in all of DSP. The FFT cannot make assumptions. Making an
> assumption is a mental activity. Only a living creature with
> a brain can make an assumption.
I suppose so.
But consider that the Fourier series is made up as a sum of
periodic functions with the same period. Mathematically, the sum
is also periodic with that period.
So, who is making assumptions?
There are transforms with other properties, but Fourier chose those
functions when making the Fourier series. Does that move Fourier's
assuming into the transform?
Why can only living creatures with a brain make assumptions?
Can robots with an electronic brain make assumptions? Or are the
assumptions built-in by the designers and builders of the robot?
Now consider a robot constructed to do some operation given some
inputs, and maybe stretching it somewhat, the Fourier series is a
robot that, given some input gives some other output. The assumptions
that went into its design determine those outputs. To me, it isn't so
hard to say that the robot makes assumptions based on the properties
given to it by its designer.
Even more, what is it that gives biochemical brains the ability to
make assumptions but electronic ones don't have that ability?
Both are built out of quantum-mechanical atoms and molecules,
yet we give special properties to some, and not to others.
Reply by ●January 27, 20202020-01-27
On Tuesday, December 17, 2019 at 5:36:07 AM UTC-8, Richard (Rick) Lyons wrote:
(snip)
> Hi Dale (and Steve Pope). The notion of periodicity is much more
> complicated than we first thought when we began to learn DSP theory.
> College DSP textbooks say that an x(n) sequence has a period of
> N samples if and only if:
> x[n+N] = x[n] for all n.
> But that equality is ONLY true for infinite-length sequences,
> and infinite-length sequences do not exist in reality.
> An infinite-length sequence is an abstract idea, ...like a perfect
> circle or one of Euclid's lines having infinite length and
> zero thickness. What this means is that, based on the above
> periodicity definition, we will never encounter, nor ever
> be able to generate, a periodic sequence in our real world.
This is bad, as much of physics, especially quantum mechanics,
depends on Fourier transforms with t from -infinity to +infinity,
or in higher dimension, over all space.
Reply by ●January 27, 20202020-01-27
On Thursday, December 26, 2019 at 1:29:45 PM UTC-8, Randy Yates wrote:
(sni, someone wrote)
> > I THOUGHT IT DID.
> (emphasis mine)
> Well now that's interesting. Can you show me the number "3" Rick? I
> don't mean one of a number of "representations" of the number "3," e.g.,
> using Roman numerals written in blue ink pen on one of Ziggy's thank-you
> notes in your handwriting (possibly while slightly intoxicated), but:
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> THE ONE AND ONLY NUMBER "3."
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Reminds me of the proof that there is no least interesting number.
1: Assume that there is a least interesting number.
2: That number would be very interesting, as it has a property
that no other number has.
3: So it isn't least interesting after all.
And definitely it isn't the number 3.
Reply by Randy Yates●December 29, 20192019-12-29
"Richard (Rick) Lyons" <r.lyons@ieee.org> writes:
> On Thursday, December 26, 2019 at 1:29:45 PM UTC-8, Randy Yates wrote:
>>
>> Well now that's interesting. Can you show me the number "3" Rick? I
>> don't mean one of a number of "representations" of the number "3," e.g.,
>> using Roman numerals written in blue ink pen on one of Ziggy's thank-you
>> notes in your handwriting (possibly while slightly intoxicated), but:
>>
>> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>> THE ONE AND ONLY NUMBER "3."
>> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>>
>> Betcha can't.
>>
>> In my book, that makes it abstract: only a concept; not existing in the
>> real world.
>
> Hi Randy. Over the last few days I've been thinkin' about
> the question, "Does the number 3 exist?" My current opinion
> is: No. The number 3 does not exist.
>
> But this whole discussion troubles me because (don't laugh
> at me) I believe Santa Claus exists. So now you'll ask me,
> "How could Santa Claus exist but the number 3 does not exist?"
> I have to think more about all of this.
>
>> And that was my point: if you insist that one concept must be dismissed
>> solely because it is abstract, you must dismiss them all, and this would
>> lead to a total breakdown of science, physics, and mathematics as we
>> know them today.
>
> Wait, I didn't say that abstract ideas should be dismissed.
> The abstract notion of a perfect circle is a useful idea in
> math field of geometry. And the same can be said for the
> abstract notion of one of Euclid's lines having infinite
> length and zero thickness.
>
>> So perhaps it would be good to rethink periodicity and infinite-length
>> sequences.
>
> My main point was that the college textbook definition
> of "periodicity" does not apply to any discrete sequence
> that we will ever encounter (or ever generate) in practice.
Well, yeah, that's true. There are no infinite-length sequences in
reality. There are no lines in reality. There are no circles in reality.
There are no Dirac delta functions in reality. Sinusoids don't exist.
Etc., etc.
What of it? How is this fact pertinent to your point?
In fact, color me thick, but I'm not exactly sure what your point even
is. Can you please break it down to simple (but accurate) terms for me?
>> Finally, I must thank you for expanding my vocabulary: I don't remember
>> ever hearing of the word "rapscallion" before this. Thank you! I am
>> not sure if I'm OK with being referred to as one, but thanks for
>> the word anyway!
>
> NO OFFENSE INTENDED.
> My guess is that the word "rapscallion" is a couple
> of hundred years old. To me the word means "a likeable
> guy who makes innocent trouble strictly for entertainment
> purposes", i.e., one who is playfully mischievous.
> (Huckleberry Finn, the boy created by Mark Twain,
> was a rapscallion. So, ha ha, you're in good company Randy!)
Gosh, I almost feel special now... :)
--
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com
Reply by Richard (Rick) Lyons●December 29, 20192019-12-29
On Thursday, December 26, 2019 at 1:29:45 PM UTC-8, Randy Yates wrote:
>
> Well now that's interesting. Can you show me the number "3" Rick? I
> don't mean one of a number of "representations" of the number "3," e.g.,
> using Roman numerals written in blue ink pen on one of Ziggy's thank-you
> notes in your handwriting (possibly while slightly intoxicated), but:
>
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> THE ONE AND ONLY NUMBER "3."
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>
> Betcha can't.
>
> In my book, that makes it abstract: only a concept; not existing in the
> real world.
Hi Randy. Over the last few days I've been thinkin' about
the question, "Does the number 3 exist?" My current opinion
is: No. The number 3 does not exist.
But this whole discussion troubles me because (don't laugh
at me) I believe Santa Claus exists. So now you'll ask me,
"How could Santa Claus exist but the number 3 does not exist?"
I have to think more about all of this.
> And that was my point: if you insist that one concept must be dismissed
> solely because it is abstract, you must dismiss them all, and this would
> lead to a total breakdown of science, physics, and mathematics as we
> know them today.
Wait, I didn't say that abstract ideas should be dismissed.
The abstract notion of a perfect circle is a useful idea in
math field of geometry. And the same can be said for the
abstract notion of one of Euclid's lines having infinite
length and zero thickness.
> So perhaps it would be good to rethink periodicity and infinite-length
> sequences.
My main point was that the college textbook definition
of "periodicity" does not apply to any discrete sequence
that we will ever encounter (or ever generate) in practice.
> Finally, I must thank you for expanding my vocabulary: I don't remember
> ever hearing of the word "rapscallion" before this. Thank you! I am
> not sure if I'm OK with being referred to as one, but thanks for
> the word anyway!
NO OFFENSE INTENDED.
My guess is that the word "rapscallion" is a couple
of hundred years old. To me the word means "a likeable
guy who makes innocent trouble strictly for entertainment
purposes", i.e., one who is playfully mischievous.
(Huckleberry Finn, the boy created by Mark Twain,
was a rapscallion. So, ha ha, you're in good company Randy!)
Reply by Randy Yates●December 26, 20192019-12-26
"Richard (Rick) Lyons" <r.lyons@ieee.org> writes:
> On Friday, December 20, 2019 at 9:31:12 PM UTC-8, Randy Yates wrote:
>> "Richard (Rick) Lyons" <r.lyons@ieee.org> writes:
>>
>> > On Monday, December 16, 2019 at 9:13:02 PM UTC-8, dbd wrote:
>> >>
>> >> The evangelists who wish to interpret the output of the DFT as samples of the Fourier Transform must assume that the input is periodic in the DFT size.
>> >>
>> >> Dale B Dalrymple
>> >
>> > Hi Dale (and Steve Pope). The notion of periodicity is much more
>> > complicated than we first thought when we began to learn DSP
>> > theory. College DSP textbooks say that an x(n) sequence has a
>> > period of N samples if and only if:
>> >
>> > x[n+N] = x[n] for all n.
>> >
>> > But that equality is ONLY true for infinite-length sequences, and
>> > infinite-length sequences do not exist in reality.
>>
>> Neither do numbers.
>> --
>> Randy Yates
>
> Randy, ...you rapscallion!! Ha ha.
> Now you're forcing me to decide if the number 3 exists.
> I THOUGHT IT DID.
(emphasis mine)
Well now that's interesting. Can you show me the number "3" Rick? I
don't mean one of a number of "representations" of the number "3," e.g.,
using Roman numerals written in blue ink pen on one of Ziggy's thank-you
notes in your handwriting (possibly while slightly intoxicated), but:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
THE ONE AND ONLY NUMBER "3."
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Betcha can't.
In my book, that makes it abstract: only a concept; not existing in the
real world.
And that was my point: if you insist that one concept must be dismissed
solely because it is abstract, you must dismiss them all, and this would
lead to a total breakdown of science, physics, and mathematics as we
know them today.
So perhaps it would be good to rethink periodicity and infinite-length
sequences.
> [...]
> Randy, does the musical note "middle C" exist?
Well, it depends on what you mean by "middle C." If you mean a note with
the exact frequency 440 * (2^(1/12))^3 Hz, then no (please, let's not
get into temperaments!).
If you mean the 3rd white note C from the lowest C on a piano, then yes
(on most pianos).
Finally, I must thank you for expanding my vocabulary: I don't remember
ever hearing of the word "rapscallion" before this. Thank you! I am
not sure if I'm OK with being referred to as one, but thanks for
the word anyway!
--
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com
Reply by Steve Pope●December 22, 20192019-12-22
Eric Jacobsen <theman@ericjacobsen.org> wrote:
>On Sat, 21 Dec 2019 21:45:31 +0000 (UTC), spope384@gmail.com (Steve
>Pope) wrote:
>>(The inclusion of a DFT is not a premise of this discussion?)
>AFAICT the context is periodicity over the aperture of a DFT.
Yes, right. I was addessing only the sub-dicussion started by
Rick, regarding the "notion of periodicity". Here Rick envisions
two as-yet-undescribed algorithms for analyzing this.
Those algorithms are not described as using transforms, and so
could be pure time-domain algorithms, as is the case with my
subsequent comments.
The original thread, yes, is about using transforms.
Sorry for being unclear.
Steve
Reply by Eric Jacobsen●December 21, 20192019-12-21
On Sat, 21 Dec 2019 21:45:31 +0000 (UTC), spope384@gmail.com (Steve
Pope) wrote:
>Eric Jacobsen <theman@ericjacobsen.org> wrote:
>
>>On Fri, 20 Dec 2019 02:59:37 +0000 (UTC), spope384@gmail.com (Steve
>
>>>>>> [Rick describes a sigal]
>
>>>>> The signal is short-term stationary and is also narrowband, and not
>>>>> noise-like. These may add up to it being "quasi-periodic", or some such.
>
>>>>The signal can be as noise-like as any sequence of only N samples can
>>>>be.
>
>>>Yes, I agree. (Although the specific signal described by Rick is
>>>not noise-like.)
>
>>>I think of "noise-like" as suggesting the signal contains little to no
>>>information and little to no autocorrelation. In that sense, one
>>>can make the signal more noise-like by randomising the sign, phase,
>>>or some other property of each repetition... which of course makes
>>>it not periodic, or less "quasi-periodic" than it was before.
>
>>Probably most of us generally think of noise along those lines, but
>>one definition of "noise" that I've seen is "any unwanted signal".
>
>Okay.
>
>>There are plenty of cases where a very pure tone would be a
>>significant impairment and perhaps treated as "noise". In a
>>spread-spectrum system, a tone will turn into pseudo-noise after the
>>despreader.
>
>Yes, and interleaving can turn bursty noise/interference into something
>that behaves more like non-bursty noise/interference.
>
>>And back to Dale's point, it doesn't really matter. The DFT treats
>>all of it the same.
>
>(The inclusion of a DFT is not a premise of this discussion?)
AFAICT the context is periodicity over the aperture of a DFT.
>Whether it matters: for lots of applications it does. I first encountered
>the idea of a signal analysis providing a metric of "tone like" vs.
>"noise like" in a discussion with Bob Orban -- must have been around
>1979 -- it was definitely needed in his audio products, many other audio
>products, and things like vocoders.
>
>In communications .. well, such distinctions also matter, of course,
>but if the local word usage considers all interferers to be "noise",
>(valid terminology), then you need a term other than "noise-like" for
>these sorts of distinctions.
>
>Steve
This is pretty normal in the usual context of ambiguous or overlapping
definitions of engineering terms and DSP and comm terms in particular.
This is why I cited the particular outlier definition of "noise",
since one assumes what is meant at one's peril if it is not clarified
by something like "AWGN", which does imply specific characteristics.
Otherwise you might not know for certain what kind of "noise" might be
meant.
Especially in things like audio, many non-engineers would call loud,
intrusive tones, "noise". You and I might not, but I've also seen a
lot of correlated things called "noise", like harmonic interference,
etc., etc., if it presents an impairment. Quantization "noise" is
often highly correlated, but we call it "noise", anyway.
I just thought it was in context of the discussion of noise being
periodic or phase-locked over a DFT aperture, that if an otherwise
reasonably stochastic signal is impaired by a tone with an integer
number of cycles over the aperture, it might fit the description of
"noise" even if sinusoidal.
Reply by Steve Pope●December 21, 20192019-12-21
Eric Jacobsen <theman@ericjacobsen.org> wrote:
>On Fri, 20 Dec 2019 02:59:37 +0000 (UTC), spope384@gmail.com (Steve
>>>>> [Rick describes a sigal]
>>>> The signal is short-term stationary and is also narrowband, and not
>>>> noise-like. These may add up to it being "quasi-periodic", or some such.
>>>The signal can be as noise-like as any sequence of only N samples can
>>>be.
>>Yes, I agree. (Although the specific signal described by Rick is
>>not noise-like.)
>>I think of "noise-like" as suggesting the signal contains little to no
>>information and little to no autocorrelation. In that sense, one
>>can make the signal more noise-like by randomising the sign, phase,
>>or some other property of each repetition... which of course makes
>>it not periodic, or less "quasi-periodic" than it was before.
>Probably most of us generally think of noise along those lines, but
>one definition of "noise" that I've seen is "any unwanted signal".
Okay.
>There are plenty of cases where a very pure tone would be a
>significant impairment and perhaps treated as "noise". In a
>spread-spectrum system, a tone will turn into pseudo-noise after the
>despreader.
Yes, and interleaving can turn bursty noise/interference into something
that behaves more like non-bursty noise/interference.
>And back to Dale's point, it doesn't really matter. The DFT treats
>all of it the same.
(The inclusion of a DFT is not a premise of this discussion?)
Whether it matters: for lots of applications it does. I first encountered
the idea of a signal analysis providing a metric of "tone like" vs.
"noise like" in a discussion with Bob Orban -- must have been around
1979 -- it was definitely needed in his audio products, many other audio
products, and things like vocoders.
In communications .. well, such distinctions also matter, of course,
but if the local word usage considers all interferers to be "noise",
(valid terminology), then you need a term other than "noise-like" for
these sorts of distinctions.
Steve
Reply by Eric Jacobsen●December 21, 20192019-12-21
On Sat, 21 Dec 2019 00:31:05 -0500, Randy Yates
<yates@digitalsignallabs.com> wrote:
>"Richard (Rick) Lyons" <r.lyons@ieee.org> writes:
>
>> On Monday, December 16, 2019 at 9:13:02 PM UTC-8, dbd wrote:
>>>
>>> The evangelists who wish to interpret the output of the DFT as samples of the Fourier Transform must assume that the input is periodic in the DFT size.
>>>
>>> Dale B Dalrymple
>>
>> Hi Dale (and Steve Pope). The notion of periodicity is much more complicated than we first thought when we began to learn DSP theory. College DSP textbooks say that an x(n) sequence has a period of N samples if and only if:
>>
>> x[n+N] = x[n] for all n.
>>
>> But that equality is ONLY true for infinite-length sequences, and
>> infinite-length sequences do not exist in reality.
>
>Neither do numbers.