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Discussion of precise time and frequency measurement

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Dr Kinali

MD
Magnus Danielson
Wed, Oct 12, 2022 9:53 AM

Dear fellow time-nuts,

I just saw the PhD defense of Attila Kinali, which was succsessful and
render him being Dr. Kinali.

It is interesting in that it shows that the Fourier transform
traditionally used in engineering is not properly done as viewed in
mathematical strictness. Through the formalism of math he redefines a
Fourier transform that does work in a mathematical sense while being
consistent with the traditional one and hence useful. The key issue is
that some functions tend to integrate to infinity while they are in fact
power limited, so it's only the length of integration that scales them
to infinity. This is where engineering use cheats but a math strict
approach cannot cheat.

He also visited a look at noise models and how these affect predicitions
of noise of out amplifiers, with illustrations on how that now is used
to better model actual noise performance.

Further he analysed meta stability of digital circuits and discussed those.

Overall an impressive thesis, not to say there is not to research on, as
there is and several topics was discussed durign the defense, as it should.

Congratulations! Very well executed and performed!

Had conditions been better, I would have been physically present as
originally planned.

Cheers,
Magnus

Dear fellow time-nuts, I just saw the PhD defense of Attila Kinali, which was succsessful and render him being Dr. Kinali. It is interesting in that it shows that the Fourier transform traditionally used in engineering is not properly done as viewed in mathematical strictness. Through the formalism of math he redefines a Fourier transform that does work in a mathematical sense while being consistent with the traditional one and hence useful. The key issue is that some functions tend to integrate to infinity while they are in fact power limited, so it's only the length of integration that scales them to infinity. This is where engineering use cheats but a math strict approach cannot cheat. He also visited a look at noise models and how these affect predicitions of noise of out amplifiers, with illustrations on how that now is used to better model actual noise performance. Further he analysed meta stability of digital circuits and discussed those. Overall an impressive thesis, not to say there is not to research on, as there is and several topics was discussed durign the defense, as it should. Congratulations! Very well executed and performed! Had conditions been better, I would have been physically present as originally planned. Cheers, Magnus
SK
Steve Krull
Wed, Oct 12, 2022 11:05 PM

Congratulations, Dr. Kinali!

Attila, it was a pleasure to meet you for dinner in Koln a few years ago, and I hope the Sulzer is working well for you!

Steve K.

On Oct 12, 2022, at 5:20 AM, Magnus Danielson via time-nuts time-nuts@lists.febo.com wrote:

Dear fellow time-nuts,

I just saw the PhD defense of Attila Kinali, which was succsessful and render him being Dr. Kinali.

It is interesting in that it shows that the Fourier transform traditionally used in engineering is not properly done as viewed in mathematical strictness. Through the formalism of math he redefines a Fourier transform that does work in a mathematical sense while being consistent with the traditional one and hence useful. The key issue is that some functions tend to integrate to infinity while they are in fact power limited, so it's only the length of integration that scales them to infinity. This is where engineering use cheats but a math strict approach cannot cheat.

He also visited a look at noise models and how these affect predicitions of noise of out amplifiers, with illustrations on how that now is used to better model actual noise performance.

Further he analysed meta stability of digital circuits and discussed those.

Overall an impressive thesis, not to say there is not to research on, as there is and several topics was discussed durign the defense, as it should.

Congratulations! Very well executed and performed!

Had conditions been better, I would have been physically present as originally planned.

Cheers,
Magnus


time-nuts mailing list -- time-nuts@lists.febo.com
To unsubscribe send an email to time-nuts-leave@lists.febo.com

Congratulations, Dr. Kinali! Attila, it was a pleasure to meet you for dinner in Koln a few years ago, and I hope the Sulzer is working well for you! Steve K. > On Oct 12, 2022, at 5:20 AM, Magnus Danielson via time-nuts <time-nuts@lists.febo.com> wrote: > > Dear fellow time-nuts, > > I just saw the PhD defense of Attila Kinali, which was succsessful and render him being Dr. Kinali. > > It is interesting in that it shows that the Fourier transform traditionally used in engineering is not properly done as viewed in mathematical strictness. Through the formalism of math he redefines a Fourier transform that does work in a mathematical sense while being consistent with the traditional one and hence useful. The key issue is that some functions tend to integrate to infinity while they are in fact power limited, so it's only the length of integration that scales them to infinity. This is where engineering use cheats but a math strict approach cannot cheat. > > He also visited a look at noise models and how these affect predicitions of noise of out amplifiers, with illustrations on how that now is used to better model actual noise performance. > > Further he analysed meta stability of digital circuits and discussed those. > > Overall an impressive thesis, not to say there is not to research on, as there is and several topics was discussed durign the defense, as it should. > > Congratulations! Very well executed and performed! > > Had conditions been better, I would have been physically present as originally planned. > > Cheers, > Magnus > _______________________________________________ > time-nuts mailing list -- time-nuts@lists.febo.com > To unsubscribe send an email to time-nuts-leave@lists.febo.com
MB
Martin Burnicki
Thu, Oct 13, 2022 7:36 AM

Congratulation, Attila!

I was very happy to hear this, and thanks Magnus for letting us know!

Martin

Magnus Danielson via time-nuts wrote:

Dear fellow time-nuts,

I just saw the PhD defense of Attila Kinali, which was succsessful and
render him being Dr. Kinali.

It is interesting in that it shows that the Fourier transform
traditionally used in engineering is not properly done as viewed in
mathematical strictness. Through the formalism of math he redefines a
Fourier transform that does work in a mathematical sense while being
consistent with the traditional one and hence useful. The key issue is
that some functions tend to integrate to infinity while they are in fact
power limited, so it's only the length of integration that scales them
to infinity. This is where engineering use cheats but a math strict
approach cannot cheat.

He also visited a look at noise models and how these affect predicitions
of noise of out amplifiers, with illustrations on how that now is used
to better model actual noise performance.

Further he analysed meta stability of digital circuits and discussed those.

Overall an impressive thesis, not to say there is not to research on, as
there is and several topics was discussed durign the defense, as it should.

Congratulations! Very well executed and performed!

Had conditions been better, I would have been physically present as
originally planned.

Cheers,
Magnus


time-nuts mailing list -- time-nuts@lists.febo.com
To unsubscribe send an email to time-nuts-leave@lists.febo.com

Congratulation, Attila! I was very happy to hear this, and thanks Magnus for letting us know! Martin Magnus Danielson via time-nuts wrote: > Dear fellow time-nuts, > > I just saw the PhD defense of Attila Kinali, which was succsessful and > render him being Dr. Kinali. > > It is interesting in that it shows that the Fourier transform > traditionally used in engineering is not properly done as viewed in > mathematical strictness. Through the formalism of math he redefines a > Fourier transform that does work in a mathematical sense while being > consistent with the traditional one and hence useful. The key issue is > that some functions tend to integrate to infinity while they are in fact > power limited, so it's only the length of integration that scales them > to infinity. This is where engineering use cheats but a math strict > approach cannot cheat. > > He also visited a look at noise models and how these affect predicitions > of noise of out amplifiers, with illustrations on how that now is used > to better model actual noise performance. > > Further he analysed meta stability of digital circuits and discussed those. > > Overall an impressive thesis, not to say there is not to research on, as > there is and several topics was discussed durign the defense, as it should. > > Congratulations! Very well executed and performed! > > Had conditions been better, I would have been physically present as > originally planned. > > Cheers, > Magnus > _______________________________________________ > time-nuts mailing list -- time-nuts@lists.febo.com > To unsubscribe send an email to time-nuts-leave@lists.febo.com
DD
Dr. David Kirkby
Thu, Oct 13, 2022 8:08 AM

On Wed, 12 Oct 2022 at 11:20, Magnus Danielson via time-nuts <
time-nuts@lists.febo.com> wrote:

Dear fellow time-nuts,

I just saw the PhD defense of Attila Kinali, which was succsessful and
render him being Dr. Kinali.

Congratulations to Dr. Kinali. Is your thesis available for download? I
would like to think that electronic downloads would be available for all
PhDs, but that doesn’t seem to be the case.

Dave.

--
Dr. David Kirkby,
Kirkby Microwave Ltd,
drkirkby@kirkbymicrowave.co.uk
https://www.kirkbymicrowave.co.uk/
Telephone 01621-680100./ +44 1621 680100

Registered in England & Wales, company number 08914892.
Registered office:
Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, United
Kingdom

On Wed, 12 Oct 2022 at 11:20, Magnus Danielson via time-nuts < time-nuts@lists.febo.com> wrote: > Dear fellow time-nuts, > > I just saw the PhD defense of Attila Kinali, which was succsessful and > render him being Dr. Kinali. Congratulations to Dr. Kinali. Is your thesis available for download? I would like to think that electronic downloads would be available for all PhDs, but that doesn’t seem to be the case. Dave. -- Dr. David Kirkby, Kirkby Microwave Ltd, drkirkby@kirkbymicrowave.co.uk https://www.kirkbymicrowave.co.uk/ Telephone 01621-680100./ +44 1621 680100 Registered in England & Wales, company number 08914892. Registered office: Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, United Kingdom
MD
Magnus Danielson
Thu, Oct 13, 2022 8:37 AM

Dear David,

On 2022-10-13 10:08, Dr. David Kirkby wrote:

On Wed, 12 Oct 2022 at 11:20, Magnus Danielson via time-nuts
time-nuts@lists.febo.com wrote:

 Dear fellow time-nuts,

 I just saw the PhD defense of Attila Kinali, which was succsessful
 and
 render him being Dr. Kinali.

Congratulations to Dr. Kinali. Is your thesis available for download?
I would like to think that electronic downloads would be available for
all PhDs, but that doesn’t seem to be the case.

Dr. Kinali has a few things to attend to before he can publish the final
version, but you should be given in in a few days. It will come.

Cheers,
Magnus

Dave.

--
Dr. David Kirkby,
Kirkby Microwave Ltd,
drkirkby@kirkbymicrowave.co.uk
https://www.kirkbymicrowave.co.uk/
Telephone 01621-680100./ +44 1621 680100

Registered in England & Wales, company number 08914892.
Registered office:
Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT,
United Kingdom

Dear David, On 2022-10-13 10:08, Dr. David Kirkby wrote: > On Wed, 12 Oct 2022 at 11:20, Magnus Danielson via time-nuts > <time-nuts@lists.febo.com> wrote: > > Dear fellow time-nuts, > > I just saw the PhD defense of Attila Kinali, which was succsessful > and > render him being Dr. Kinali. > > > Congratulations to Dr. Kinali. Is your thesis available for download? > I would like to think that electronic downloads would be available for > all PhDs, but that doesn’t seem to be the case. Dr. Kinali has a few things to attend to before he can publish the final version, but you should be given in in a few days. It will come. Cheers, Magnus > > Dave. > > -- > Dr. David Kirkby, > Kirkby Microwave Ltd, > drkirkby@kirkbymicrowave.co.uk > https://www.kirkbymicrowave.co.uk/ > Telephone 01621-680100./ +44 1621 680100 > > Registered in England & Wales, company number 08914892. > Registered office: > Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, > United Kingdom
MD
Magnus Danielson
Thu, Oct 13, 2022 8:40 AM

Dear Martin,

Thanks. I think it is important to celebrate efforts like these, there
is over 7 years of hard work behind it. As you read it, you will find it
addressing hard issues.

Cheers,
Magnus

On 2022-10-13 09:36, Martin Burnicki wrote:

Congratulation, Attila!

I was very happy to hear this, and thanks Magnus for letting us know!

Martin

Magnus Danielson via time-nuts wrote:

Dear fellow time-nuts,

I just saw the PhD defense of Attila Kinali, which was succsessful
and render him being Dr. Kinali.

It is interesting in that it shows that the Fourier transform
traditionally used in engineering is not properly done as viewed in
mathematical strictness. Through the formalism of math he redefines a
Fourier transform that does work in a mathematical sense while being
consistent with the traditional one and hence useful. The key issue
is that some functions tend to integrate to infinity while they are
in fact power limited, so it's only the length of integration that
scales them to infinity. This is where engineering use cheats but a
math strict approach cannot cheat.

He also visited a look at noise models and how these affect
predicitions of noise of out amplifiers, with illustrations on how
that now is used to better model actual noise performance.

Further he analysed meta stability of digital circuits and discussed
those.

Overall an impressive thesis, not to say there is not to research on,
as there is and several topics was discussed durign the defense, as
it should.

Congratulations! Very well executed and performed!

Had conditions been better, I would have been physically present as
originally planned.

Cheers,
Magnus


time-nuts mailing list -- time-nuts@lists.febo.com
To unsubscribe send an email to time-nuts-leave@lists.febo.com

Dear Martin, Thanks. I think it is important to celebrate efforts like these, there is over 7 years of hard work behind it. As you read it, you will find it addressing hard issues. Cheers, Magnus On 2022-10-13 09:36, Martin Burnicki wrote: > Congratulation, Attila! > > I was very happy to hear this, and thanks Magnus for letting us know! > > Martin > > > Magnus Danielson via time-nuts wrote: >> Dear fellow time-nuts, >> >> I just saw the PhD defense of Attila Kinali, which was succsessful >> and render him being Dr. Kinali. >> >> It is interesting in that it shows that the Fourier transform >> traditionally used in engineering is not properly done as viewed in >> mathematical strictness. Through the formalism of math he redefines a >> Fourier transform that does work in a mathematical sense while being >> consistent with the traditional one and hence useful. The key issue >> is that some functions tend to integrate to infinity while they are >> in fact power limited, so it's only the length of integration that >> scales them to infinity. This is where engineering use cheats but a >> math strict approach cannot cheat. >> >> He also visited a look at noise models and how these affect >> predicitions of noise of out amplifiers, with illustrations on how >> that now is used to better model actual noise performance. >> >> Further he analysed meta stability of digital circuits and discussed >> those. >> >> Overall an impressive thesis, not to say there is not to research on, >> as there is and several topics was discussed durign the defense, as >> it should. >> >> Congratulations! Very well executed and performed! >> >> Had conditions been better, I would have been physically present as >> originally planned. >> >> Cheers, >> Magnus >> _______________________________________________ >> time-nuts mailing list -- time-nuts@lists.febo.com >> To unsubscribe send an email to time-nuts-leave@lists.febo.com >
MW
Mathias Weyland
Thu, Oct 13, 2022 8:48 AM

On 2022-10-12 11:53, Magnus Danielson via time-nuts wrote:

Good morning

I just saw the PhD defense of Attila Kinali, which was succsessful and
render him being Dr. Kinali.

Congratulations Attila! You have been a strong inspiration to me when I
was growing up  and it is cheering to learn that you have not changed.
Please enjoy your success.

Matt

On 2022-10-12 11:53, Magnus Danielson via time-nuts wrote: Good morning > I just saw the PhD defense of Attila Kinali, which was succsessful and > render him being Dr. Kinali. Congratulations Attila! You have been a strong inspiration to me when I was growing up and it is cheering to learn that you have not changed. Please enjoy your success. Matt
BK
Bob kb8tq
Thu, Oct 13, 2022 11:32 AM

Hi

Very cool !!

Bob

On Oct 12, 2022, at 5:53 AM, Magnus Danielson via time-nuts time-nuts@lists.febo.com wrote:

Dear fellow time-nuts,

I just saw the PhD defense of Attila Kinali, which was succsessful and render him being Dr. Kinali.

It is interesting in that it shows that the Fourier transform traditionally used in engineering is not properly done as viewed in mathematical strictness. Through the formalism of math he redefines a Fourier transform that does work in a mathematical sense while being consistent with the traditional one and hence useful. The key issue is that some functions tend to integrate to infinity while they are in fact power limited, so it's only the length of integration that scales them to infinity. This is where engineering use cheats but a math strict approach cannot cheat.

He also visited a look at noise models and how these affect predicitions of noise of out amplifiers, with illustrations on how that now is used to better model actual noise performance.

Further he analysed meta stability of digital circuits and discussed those.

Overall an impressive thesis, not to say there is not to research on, as there is and several topics was discussed durign the defense, as it should.

Congratulations! Very well executed and performed!

Had conditions been better, I would have been physically present as originally planned.

Cheers,
Magnus


time-nuts mailing list -- time-nuts@lists.febo.com
To unsubscribe send an email to time-nuts-leave@lists.febo.com

Hi Very cool !! Bob > On Oct 12, 2022, at 5:53 AM, Magnus Danielson via time-nuts <time-nuts@lists.febo.com> wrote: > > Dear fellow time-nuts, > > I just saw the PhD defense of Attila Kinali, which was succsessful and render him being Dr. Kinali. > > It is interesting in that it shows that the Fourier transform traditionally used in engineering is not properly done as viewed in mathematical strictness. Through the formalism of math he redefines a Fourier transform that does work in a mathematical sense while being consistent with the traditional one and hence useful. The key issue is that some functions tend to integrate to infinity while they are in fact power limited, so it's only the length of integration that scales them to infinity. This is where engineering use cheats but a math strict approach cannot cheat. > > He also visited a look at noise models and how these affect predicitions of noise of out amplifiers, with illustrations on how that now is used to better model actual noise performance. > > Further he analysed meta stability of digital circuits and discussed those. > > Overall an impressive thesis, not to say there is not to research on, as there is and several topics was discussed durign the defense, as it should. > > Congratulations! Very well executed and performed! > > Had conditions been better, I would have been physically present as originally planned. > > Cheers, > Magnus > _______________________________________________ > time-nuts mailing list -- time-nuts@lists.febo.com > To unsubscribe send an email to time-nuts-leave@lists.febo.com
PS
paul swed
Thu, Oct 13, 2022 4:59 PM

Very happy for Dr. Kinali. He has share great insights with the time-nuts
and I have learned a lot from reading his posts.
Congratulations.
Paul
WB8TSL

On Thu, Oct 13, 2022 at 12:55 PM Bob kb8tq via time-nuts <
time-nuts@lists.febo.com> wrote:

Hi

Very cool !!

Bob

On Oct 12, 2022, at 5:53 AM, Magnus Danielson via time-nuts <

Dear fellow time-nuts,

I just saw the PhD defense of Attila Kinali, which was succsessful and

render him being Dr. Kinali.

It is interesting in that it shows that the Fourier transform

traditionally used in engineering is not properly done as viewed in
mathematical strictness. Through the formalism of math he redefines a
Fourier transform that does work in a mathematical sense while being
consistent with the traditional one and hence useful. The key issue is that
some functions tend to integrate to infinity while they are in fact power
limited, so it's only the length of integration that scales them to
infinity. This is where engineering use cheats but a math strict approach
cannot cheat.

He also visited a look at noise models and how these affect predicitions

of noise of out amplifiers, with illustrations on how that now is used to
better model actual noise performance.

Further he analysed meta stability of digital circuits and discussed

those.

Overall an impressive thesis, not to say there is not to research on, as

there is and several topics was discussed durign the defense, as it should.

Congratulations! Very well executed and performed!

Had conditions been better, I would have been physically present as

originally planned.

Cheers,
Magnus


time-nuts mailing list -- time-nuts@lists.febo.com
To unsubscribe send an email to time-nuts-leave@lists.febo.com


time-nuts mailing list -- time-nuts@lists.febo.com
To unsubscribe send an email to time-nuts-leave@lists.febo.com

Very happy for Dr. Kinali. He has share great insights with the time-nuts and I have learned a lot from reading his posts. Congratulations. Paul WB8TSL On Thu, Oct 13, 2022 at 12:55 PM Bob kb8tq via time-nuts < time-nuts@lists.febo.com> wrote: > Hi > > Very cool !! > > Bob > > > On Oct 12, 2022, at 5:53 AM, Magnus Danielson via time-nuts < > time-nuts@lists.febo.com> wrote: > > > > Dear fellow time-nuts, > > > > I just saw the PhD defense of Attila Kinali, which was succsessful and > render him being Dr. Kinali. > > > > It is interesting in that it shows that the Fourier transform > traditionally used in engineering is not properly done as viewed in > mathematical strictness. Through the formalism of math he redefines a > Fourier transform that does work in a mathematical sense while being > consistent with the traditional one and hence useful. The key issue is that > some functions tend to integrate to infinity while they are in fact power > limited, so it's only the length of integration that scales them to > infinity. This is where engineering use cheats but a math strict approach > cannot cheat. > > > > He also visited a look at noise models and how these affect predicitions > of noise of out amplifiers, with illustrations on how that now is used to > better model actual noise performance. > > > > Further he analysed meta stability of digital circuits and discussed > those. > > > > Overall an impressive thesis, not to say there is not to research on, as > there is and several topics was discussed durign the defense, as it should. > > > > Congratulations! Very well executed and performed! > > > > Had conditions been better, I would have been physically present as > originally planned. > > > > Cheers, > > Magnus > > _______________________________________________ > > time-nuts mailing list -- time-nuts@lists.febo.com > > To unsubscribe send an email to time-nuts-leave@lists.febo.com > _______________________________________________ > time-nuts mailing list -- time-nuts@lists.febo.com > To unsubscribe send an email to time-nuts-leave@lists.febo.com >
AK
Attila Kinali
Tue, Oct 18, 2022 1:27 PM

A wonderful good afternoon everyone!

On Wed, 12 Oct 2022 11:53:17 +0200
Magnus Danielson via time-nuts time-nuts@lists.febo.com wrote:

I just saw the PhD defense of Attila Kinali, which was succsessful and
render him being Dr. Kinali.

Thanks everyone for all the wellwishes.

As promised, I put my thesis online, which you can find at [1].
And of course it is in English... I'm insane but not insane
enough to write in German ;-)

The thesis is split into three parts.

The first part deals with the Fourier transform of signals that have infinite
energy (i.e. all signals of infinite length). In particular, the Fourier transform
is modified to work with these signals properly. The matching inverse Fourier
transform is introduced. And of course proofs that all this works as one would
expect to. But be warned, the math is dense and the write-up is less than
ideal, to put it mildly.
I then use this modified Fourier transform to define noise and 1/f^a noise
in a way that it works both in time and frequency domain, while having all
the properties we usually attribute with these types of noises.

If you deal with power spectral densities and other types of Fourier transform
type analysis of signals, you should definitely look at this part.
This part was written to correct about a century of EE literature that deals
with infinite energy signals in a mathematically incorrect way. If you have
a textbook that does not explicity handle infinte energy signals or does not
warn that the math does not work for those, chances are that the book has mistakes
in the math, if it isn't outright wrong (guess how I know).

The second part is basically a summary of the noise propagation in amplifiers
and other non-linear electronics that I have written earlier. If you have not
seen it yet, this is probably the part of my thesis with the most practical
application and impact. In short summary, it explains and extends Enrico
Rubiola's φ-type and x-type noise model and allows accurate noise predictions
in various types of circuits. In particular it explains why all noise models
of amplifiers only ever model additive noise, but noise figures are always
given in dB, i.e. are multiplicative noise.

The third part deals with fault-tolerant clock synchronization and the
metastable effects that occur when you try to do that as quickly as
possible. This part is probably the least interesting to the time-nuts
community. So feel free to skip it.

If you have any comments or question, please don't hesitate to contact me
on or off list.

Greetings and have a nice afternoon/evening

		Attila Kinali

[1] "On Time, Time Synchronization and Noise in Time Measurement Systems",
by yours truly, 2022
http://time.kinali.ch/thesis-final-kinali.pdf

--
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
-- Richard W. Hamming, The Art of Doing Science and Engineering

A wonderful good afternoon everyone! On Wed, 12 Oct 2022 11:53:17 +0200 Magnus Danielson via time-nuts <time-nuts@lists.febo.com> wrote: > I just saw the PhD defense of Attila Kinali, which was succsessful and > render him being Dr. Kinali. Thanks everyone for all the wellwishes. As promised, I put my thesis online, which you can find at [1]. And of course it is in English... I'm insane but not insane enough to write in German ;-) The thesis is split into three parts. The first part deals with the Fourier transform of signals that have infinite energy (i.e. all signals of infinite length). In particular, the Fourier transform is modified to work with these signals properly. The matching inverse Fourier transform is introduced. And of course proofs that all this works as one would expect to. But be warned, the math is dense and the write-up is less than ideal, to put it mildly. I then use this modified Fourier transform to define noise and 1/f^a noise in a way that it works both in time and frequency domain, while having all the properties we usually attribute with these types of noises. If you deal with power spectral densities and other types of Fourier transform type analysis of signals, you should definitely look at this part. This part was written to correct about a century of EE literature that deals with infinite energy signals in a mathematically incorrect way. If you have a textbook that does not explicity handle infinte energy signals or does not warn that the math does not work for those, chances are that the book has mistakes in the math, if it isn't outright wrong (guess how I know). The second part is basically a summary of the noise propagation in amplifiers and other non-linear electronics that I have written earlier. If you have not seen it yet, this is probably the part of my thesis with the most practical application and impact. In short summary, it explains and extends Enrico Rubiola's φ-type and x-type noise model and allows accurate noise predictions in various types of circuits. In particular it explains why all noise models of amplifiers only ever model additive noise, but noise figures are always given in dB, i.e. are multiplicative noise. The third part deals with fault-tolerant clock synchronization and the metastable effects that occur when you try to do that as quickly as possible. This part is probably the least interesting to the time-nuts community. So feel free to skip it. If you have any comments or question, please don't hesitate to contact me on or off list. Greetings and have a nice afternoon/evening Attila Kinali [1] "On Time, Time Synchronization and Noise in Time Measurement Systems", by yours truly, 2022 http://time.kinali.ch/thesis-final-kinali.pdf -- In science if you know what you are doing you should not be doing it. In engineering if you do not know what you are doing you should not be doing it. -- Richard W. Hamming, The Art of Doing Science and Engineering