[<<][math][>>][..]Sun Aug 8 06:57:58 CEST 2010

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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