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Sun Aug 8 06:57:58 CEST 2010

Peak compression

For many applications that have constraints on bandwidth and dynamic
range at the same time, it is useful to be able to control the
maximal signal amplitude.

The simplest way to produce wide-band constant-amplitude pulses is to
use chirps.

Another intriguing way, when the spectral content is known, is to use
Schroeder phases[4][5].  ( Using n(n-1) phase offsets -- compare to
n^2 for Newman phases. )


Now the interesting part is that there is a _digital_ variant of this.
Here one starts from a signal with minimal dynamic range: a (PSK
modulated) binary signal.

Binary can only represent 1 and -1. When modulated as a PSK signal it
is an analog signal with a small dynamic range.  (Smallest known?  See
BER[3]).

A Barker code[2] then is a sequence that is near-orthogonal to its own
shifts, meaning that its autocorrelation has a distinct peak at
shift=0, but has maginitude <= 1 for other shifts.  (Apparently,
orthogonality is too strict a constraint).

Local refs:
Optimal Binary Sequences for Spread Spectrum Multiplexing[6].
Synthesis of Low-Peak-Factor Signals and Binary Sequences With Low Autocorrelation[7].


[1] http://en.wikipedia.org/wiki/Pulse_compression
[2] http://en.wikipedia.org/wiki/Barker_code
[3] http://en.wikipedia.org/wiki/Bit_error_rate
[4] http://books.google.be/books?id=hQ6bl3RG04sC&pg=PA290&lpg=PA290&dq=schroeder+phases&source=bl&ots=7IT7kYGcyu&sig=45_66hBv0Xxo1yw9YBlyXVU0usY&hl=nl&ei=oT5eTJ-IJIX80wSc-8XHBw&sa=X&oi=book_result&ct=result&resnum=6&ved=0CEIQ6AEwBQ#v=onepage&q=schroeder%20phases&f=false
[5] http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1054411
[6] md5://c35e337e61dfbcd980e3728768f71af4
[7] md5://9b2913693c005de2515e3efeb8548e47


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