I am trying to make sense of some awful MATLAB code. The first thing it does is mirror the signal. By that I mean it doubles the array length, then puts
a time-reversed signal at the newly created back half.
So this would have the same amplitude spectum, but what else is going on? Possibly it increases the frequency resolution, as the time length is doubled.
I wonder if the algorithm had some side effect - creating crap towards
the end, and this is swept under the carpet (which is the mirror copy).
Am 15.12.19 um 03:44 schrieb hdreck@freenet.de:
I am trying to make sense of some awful MATLAB code. The first thing
it does is mirror the signal. By that I mean it doubles the
array length, then puts a time-reversed signal at the newly created back half.
The result is the same as the discrete cosine
transform (DCT), so this code may also simply be a way to perform a DCT.
I am trying to make sense of some awful MATLAB code. The first thing it does >is mirror the signal. By that I mean it doubles the array length, then puts
a time-reversed signal at the newly created back half.
So this would have the same amplitude spectum, but what else is going on? >Possibly it increases the frequency resolution, as the time length is >doubled.
I wonder if the algorithm had some side effect - creating crap towards
the end, and this is swept under the carpet (which is the mirror copy).
Am 15.12.19 um 03:44 schrieb hdreck@freenet.de:
I am trying to make sense of some awful MATLAB code. The first thing it does >> is mirror the signal. By that I mean it doubles the array length, then puts >> a time-reversed signal at the newly created back half.
So this would have the same amplitude spectum, but what else is going on?
Possibly it increases the frequency resolution, as the time length is
doubled.
I wonder if the algorithm had some side effect - creating crap towards
the end, and this is swept under the carpet (which is the mirror copy).
It removes discontinuity at then end of the interval. The FFT assumes
that the input signal is periodic and repeats infinitely many times.
This is necessary because the Fourier transform is defined for an
infinite signal, but you only give it a finite number of samples. If
done in this way, and the first and last samples have different values,
there is a discontinuity at the boundary which results in a strong >disturbance.
Am 15.12.19 um 03:44 schrieb hdreck@freenet.de:
The FFT assumes that the input signal is periodic and
repeats infinitely many times.
On Sunday, December 15, 2019 at 1:20:36 AM UTC-8, Christian Gollwitzer wrote:
Hi.
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.
Richard (Rick) Lyons <r.lyons@ieee.org> wrote:
On Sunday, December 15, 2019 at 1:20:36 AM UTC-8, Christian Gollwitzer wrote:
Hi.
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.
"The FFT evangelists assume the input is periodic.." ??
S.
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
On Monday, December 16, 2019 at 7:58:14 PM UTC-8, Steve Pope wrote:
Richard (Rick) Lyons <r.lyons@ieee.org> wrote:
On Sunday, December 15, 2019 at 1:20:36 AM UTC-8, Christian Gollwitzer wrote:
Hi.
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.
"The FFT evangelists assume the input is periodic.." ??
S.
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
...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.
...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
As George Box said:
'Essentially, all models are wrong, but some are useful'
On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote:
Hi Dale. I interpret your words to mean: Some sequences have a strong periodic nature if:
x[n+N] = x[n] for many values of n.
On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote:
Hi Dale. I interpret your words to mean: Some sequences have a strong periodic nature if:
x[n+N] = x[n] for many values of n.
Hi Rick, I assume you meant "for many values of N" or "for all N > some
large number"
--
Best wishes,
--Phil
On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote:
Hi Dale. I interpret your words to mean: Some sequences have a strong periodic nature if:
x[n+N] = x[n] for many values of n.
Rick, I would say that in any range of n where the equation is satisfied, our data is indistinguishable from samples from a periodic sequence despite the fact that our data sequence is always finite. That means an analyst can safely act as if the datawere periodic.
Dale B. Dalrymple
Hi Dale. I agree with you. If we had a 10,000-sample sequence containing >exactly 1,000 cycles of a cosine wave, we'd definitely say that sequence
was "periodic" even though it does not satisfy the following textbook >definition of periodicity:
x[n+N] = x[n] for all n.
On Wednesday, December 18, 2019 at 8:39:42 AM UTC-8, Phil Martel wrote:
Hi Rick, I assume you meant "for many values of N" or "for all N > some
large number"
--
Best wishes,
--Phil
Hi Phil. No, I did mean "many values of n". The fixed variable N is the period (an integer measured in samples) of some sequence that appears to be periodic because it has repetitive equal-amplitude sample values separated by N samples.
In my mind I've been formulating two different definitions of "periodicity" for finite-length sequences. But I'm not yet ready to advertise those definitions to you DSP guys for fear of looking like a knucklehead.
Hey Phil, ... have you seen the following web page?
https://www.dsprelated.com/showquiz/5
Regards,
[-Rick-]
On Wednesday, December 18, 2019 at 2:24:25 AM UTC-8, Richard (Rick) Lyons w= >rote:
On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote:
=20
Hi Dale. I interpret your words to mean: Some sequences have a strong pe= >riodic nature if:
=20
x[n+N] =3D x[n] for many values of n.
Rick, I would say that in any range of n where the equation is satisfied, o= >ur data is indistinguishable from samples from a periodic sequence despite = >the fact that our data sequence is always finite. That means an analyst can=
safely act as if the data were periodic.
Real data may consist of samples of the sum of components of types like per= >iodic-in-N, periodic-not-in-N, aperiodic and stocastic. Real DSP systems ca= >n't process infinite sequences, they don't need to to justify treating data=
as containing periodic components.
As Jerry would post:
"Engineering is the art of making what you want from things you can get."
Dale B. Dalrymple
...
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.
Steve
On Thursday, December 19, 2019 at 4:04:40 AM UTC-8, Steve Pope wrote:
Richard (Rick) Lyons <r.lyons@ieee.org> wrote:
Hi Dale. I agree with you. If we had a 10,000-sample sequence containing >>> exactly 1,000 cycles of a cosine wave, we'd definitely say that sequence >>> was "periodic" even though it does not satisfy the following textbook
definition of periodicity:
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.
It also allows some parameters of the sequence to be specified in
ways very hard to achieve with an analog signal source. This is useful
to generate test signals for systems containing spectrum analysers. It
is referred to as synchronous noise.
Depending on the pre- and
post-transform processing included in the scope of the test, the data
period N may need to be far larger than the transform size being
exercised in the test.
dbd <d.dalrymple@sbcglobal.net> wrote:
On Thursday, December 19, 2019 at 4:04:40 AM UTC-8, Steve Pope wrote:
Richard (Rick) Lyons <r.lyons@ieee.org> wrote:
Hi Dale. I agree with you. If we had a 10,000-sample sequence containing >>>> exactly 1,000 cycles of a cosine wave, we'd definitely say that sequence >>>> was "periodic" even though it does not satisfy the following textbook
definition of periodicity:
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.
It also allows some parameters of the sequence to be specified in
ways very hard to achieve with an analog signal source. This is useful
to generate test signals for systems containing spectrum analysers. It
is referred to as synchronous noise.
Thanks, I had not previously heard of this term.
Depending on the pre- and
post-transform processing included in the scope of the test, the data >>period N may need to be far larger than the transform size being
exercised in the test.
Yes. Thanks.
Steve
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.
"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
"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, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com
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".
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.
And back to Dale's point, it doesn't really matter. The DFT treats
all of it the same.
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
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.
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.
[...]
Randy, does the musical note "middle C" exist?
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.
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!
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!)
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.
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."
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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.
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