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| Vladimir Vassilevsky... |
 Posted: Fri Oct 30, 2009 1:06 am |
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I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal? For the narrow bandwidth, the best solution
seems to be something like linear sweep. Is there a general solution?
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com |
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| John... |
| Posted: Fri Oct 30, 2009 1:06 am |
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On Oct 29, 5:06 pm, Vladimir Vassilevsky <nos... at (no spam) nowhere.com> wrote:
Quote: I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal? For the narrow bandwidth, the best solution
seems to be something like linear sweep. Is there a general solution?
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultanthttp://www.abvolt.com
As I recall, the guy that did some work in this area years ago is
named D. Gimlin, and the answer is quadratic. |
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| glen herrmannsfeldt... |
| Posted: Fri Oct 30, 2009 1:06 am |
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Vladimir Vassilevsky <nospam at (no spam) nowhere.com> wrote:
Quote: I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal? For the narrow bandwidth, the best solution
seems to be something like linear sweep. Is there a general solution?
Interesting question. My first thought is random phase selection.
If you put papr phase into google, you get a fair number of
hits actually related to the question.
The common use of scramblers with digital modulation methods is
an indication that random phase selection isn't bad, but it does
seem that there might be another solution.
How about if you go one by one. Start with the first at zero phase,
then add the second with the appropriate phase to minimize the peak,
then the third, etc. There might even be an analytical solution.
-- glen |
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| Jerry Avins... |
| Posted: Fri Oct 30, 2009 1:15 am |
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Vladimir Vassilevsky wrote:
Quote:
I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal? For the narrow bandwidth, the best solution
seems to be something like linear sweep. Is there a general solution?
Isn't the classical solution correlation of the returned signal with the
driving long-cycle PRNG? Make the signal bipolar by replacing 0 with -1,
then scaling as appropriate. Calibrate the speaker/microphone outdoors
over a field of wheat or hay to minimize ground reflections.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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| Eric Jacobsen... |
| Posted: Fri Oct 30, 2009 1:43 am |
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On 10/29/2009 2:06 PM, Vladimir Vassilevsky wrote:
Quote:
I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal? For the narrow bandwidth, the best solution
seems to be something like linear sweep. Is there a general solution?
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
For OFDM randomizing the phase of the subcarriers (via whitening with a
scrambler) is by far the biggest bang for the buck for PAPR reduction.
I'd suspect that'd translate to this problem well.
--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com |
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| alos... |
| Posted: Fri Oct 30, 2009 2:13 am |
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Quote:
I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal? For the narrow bandwidth, the best solution
seems to be something like linear sweep. Is there a general solution?
Actually, Zadoff-Chu sequences which are special kind of chirps seem
to have properties you are asking for.
Try this in Octave:
N =1024;
n = 0:N-1;
u = 1;
zc = exp(-j*pi*n.^2/N);
plot(abs(fft(zc)));
The only requirement is that `u` is relatively prime to N.
Since Z-C sequences have perfect impulse-like (cyclic) autocorrelation it
makes
them perfect for such measurments.
--
Regards,
Alek |
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| alos... |
| Posted: Fri Oct 30, 2009 2:22 am |
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Quote: zc = exp(-j*pi*n.^2/N);
I meant:
zc = exp(-j*pi*u*n.^2/N); |
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| dbd... |
| Posted: Fri Oct 30, 2009 4:39 pm |
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On Oct 29, 2:06 pm, Vladimir Vassilevsky <nos... at (no spam) nowhere.com> wrote:
Quote: I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal? For the narrow bandwidth, the best solution
seems to be something like linear sweep. Is there a general solution?
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultanthttp://www.abvolt.com
Boyd gives two methods:
Multitone signals with low crest factor
Boyd, S.
This paper appears in: Circuits and Systems, IEEE Transactions on; Oct
1986
Volume: 33, Issue: 10, page(s): 1018- 1022
Abstract
Using some results from the recent mathematics literature, we show how
to generate signals with perfect low-pass or bandpass spectra which
have very low crest factors (under 6 dB). An application to multitone
frequency response testing is given.
Dale B. Dalrymple |
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| dbd... |
| Posted: Fri Oct 30, 2009 4:53 pm |
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| Vladimir Vassilevsky... |
| Posted: Fri Oct 30, 2009 7:46 pm |
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alos wrote:
Quote: I am trying to design a finite length digital signal for impulse
response measurement. The signal has equal energy in every FFT bin. What
should be the distribution of the phases between the bins so the PAPR of
the signal would be minimal?
Actually, Zadoff-Chu sequences which are special kind of chirps seem
to have properties you are asking for.
Try this in Octave:
N =1024;
n = 0:N-1;
u = 1;
zc = exp(-j*pi*n.^2/N);
plot(abs(fft(zc)));
The only requirement is that `u` is relatively prime to N.
Since Z-C sequences have perfect impulse-like (cyclic) autocorrelation it
makes them perfect for such measurments.
Thank you very much for the idea.
VLV |
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| Vladimir Vassilevsky... |
| Posted: Sat Oct 31, 2009 8:34 pm |
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dbd wrote:
Thank you very much, Dale.
The article describes two simple methods which produce bandpass
multitone signals with good crest factor. That's exactly what I need.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com |
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| Jake... |
| Posted: Sat Nov 07, 2009 4:05 am |
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Quote: I am trying to design a finite length digital signal for impulse response
measurement. The signal has equal energy in every FFT bin. What should be
the distribution of the phases between the bins so the PAPR of the signal
would be minimal? For the narrow bandwidth, the best solution seems to be
something like linear sweep. Is there a general solution?
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Oh please. Don't waste our time with such trivial questions. Go read some
books. |
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| dbd... |
| Posted: Sat Nov 07, 2009 4:50 am |
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On Nov 6, 4:34 pm, Randy Yates <ya... at (no spam) ieee.org> wrote:
Quote: dbd <d... at (no spam) ieee.org> writes:
[...]
Using some results from the recent mathematics literature,
This heavy handed choice of quoting seems somewhat disingenuous Randy.
Substituting back in some of the original value of "[...]"
Multitone signals with low crest factor
Boyd, S.
This paper appears in: Circuits and Systems, IEEE Transactions on; Oct
1986
Volume: 33, Issue: 10, page(s): 1018- 1022
Abstract
Using some results from the recent mathematics literature, we show how
to generate signals with perfect low-pass or bandpass spectra which
have very low crest factors (under 6 dB). An application to multitone
frequency response testing is given.
Quote: ~30 years prior was recent? I guess recent is relative. Relative to
Pythagoras, yes, it's recent.
If I were to adopt quoting in your apparent spirit:
Quote: --
Randy Yates % "If I could save time in a bottle
Digital Signal Labs % the first thing that I'd like to do"
mailto://ya... at (no spam) ieee.org % 'Ticket To The Moon
'http://www.digitalsignallabs.com% *Time*, Electric Light Orchestra
I suppose every reader has the right to decide whether to compare
'recent' to history or the attention span of comp.dsp. Boyd, a
Stanford professor might have a greater knowledge of mathematical
history than of the attention span of comp.dsp. YMMV.
Dale B. Dalrymple |
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| Randy Yates... |
| Posted: Sat Nov 07, 2009 5:34 am |
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dbd <dbd at (no spam) ieee.org> writes:
Quote: [...]
Using some results from the recent mathematics literature,
~30 years prior was recent? I guess recent is relative. Relative to
Pythagoras, yes, it's recent.
--
Randy Yates % "Remember the good old 1980's, when
Digital Signal Labs % things were so uncomplicated?"
mailto://yates at (no spam) ieee.org % 'Ticket To The Moon'
http://www.digitalsignallabs.com % *Time*, Electric Light Orchestra |
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| Jerry Avins... |
| Posted: Sat Nov 07, 2009 5:48 am |
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Randy Yates wrote:
Quote: dbd <dbd at (no spam) ieee.org> writes:
[...]
Using some results from the recent mathematics literature,
~30 years prior was recent? I guess recent is relative. Relative to
Pythagoras, yes, it's recent.
Why, Randy! That's like yesterday to some of us. :-)
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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