mirroring a signal before FFT - why?

On Thu, 19 Dec 2019 01:32:05 -0800 (PST), dbd
<d.dalrymple@sbcglobal.net> wrote:

>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.

Yup, or circular.   ;)

That's kinda sayin' the same thing, tho...

I think when people can get to where they understand and can
effectively use the various points of view they can be more productive
as well as communicate efficiently with others working from whichever
perspective.   So don't just grab one point of view and run with it,
understand as much as you can.

>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

On Thursday, December 19, 2019 at 4:04:40 AM UTC-8, Steve Pope wrote:
> ...
.> 
.> 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

Steve

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.

Dale B. Dalrymple

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 Fri, 20 Dec 2019 02:59:37 +0000 (UTC), spope384@gmail.com (Steve
Pope) wrote:

>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.

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.

>
>>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

"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 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. (There's a famous German 19th-century 
mathematician who said "God created the integers.")
But now I have to think more about the number 3. 

Randy, does the musical note "middle C" exist?

[-Rick-]

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. 

But quantities do!   ;)

>-- 
>Randy Yates, DSP/Embedded Firmware Developer
>Digital Signal Labs
>http://www.digitalsignallabs.com

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:

>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.

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