Minimum PAPR

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

Vladimir Vassilevsky wrote:
> 
> 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.
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Vladimir Vassilevsky <nospam@nowhere.com> wrote:
 
> 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

On Oct 29, 5:06&#4294967295;pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> 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.

On 10/29/2009 2:06 PM, Vladimir Vassilevsky wrote:
>
> 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

>
>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

>zc = exp(-j*pi*n.^2/N);
I meant:
zc = exp(-j*pi*u*n.^2/N);

John wrote:

> On Oct 29, 5:06 pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> 
>>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?
>>
> 
> As I recall, the guy that did some work in this area years ago is
> named D. Gimlin, and the answer is quadratic.


Thank you for the tip!

VLV

alos wrote:

>>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

On Oct 29, 2:06 pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> 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