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In [[signal processing]], a '''Constant Amplitude Zero AutoCorrelation waveform''' ('''CAZAC''') is a periodic [[complex number|complex]]-valued [[signal (electrical engineering)|signal]] with modulus one and out-of-phase periodic (cyclic) [[autocorrelation]]s equal to zero. CAZAC sequences find application in wireless communication systems, for example in [[3GPP Long Term Evolution]] for synchronization of mobile phones with base stations. [[Zadoff–Chu sequence]]s are well-known CAZAC sequences with special properties.
== Example CAZAC Sequence ==
For a CAZAC sequence of length <math>N</math> where <math>M</math> is relatively prime to <math>N</math> the <math>k</math>th symbol <math>u_k</math> is given by:<ref>{{Cite journal|last=Chu|first=D.|date=July 1972|title=Polyphase codes with good periodic correlation properties (Corresp.)|journal=IEEE Transactions on Information Theory|volume=18|issue=4|pages=531–532|doi=10.1109/TIT.1972.1054840|issn=1557-9654}}</ref>
===Even N===
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<math>u_k = \exp \left(j \frac{M \pi k (k+1)}{N} \right)</math>
==Power Spectrum of CAZAC Sequence==
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The power spectrum of a CAZAC sequence is flat.
If we have a CAZAC sequence the time ___domain
: <math>r(\tau)=\delta(n)</math>
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: <math>\left| X(f) \right|^2 = 1/N</math>
==References==
{{Reflist}}
==External links==
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{{signal-processing-stub}}
{{mathapplied-stub}}
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