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→Complex-valued functions: add citations Tags: Reverted Visual edit: Switched |
change even symmetric to conjugate symmetric and odd symmetric to conjugate antisymmetric IAW Oppenheim & Schaefer Tag: Reverted |
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The definitions for even and odd symmetry for [[Complex number|complex-valued]] functions of a real argument are similar to the real case but involve [[complex conjugation]].<ref name=Oppenheim>
{{Cite book |last1=Oppenheim |first1=Alan V. |author-link=Alan V. Oppenheim |last2=Schafer |first2=Ronald W. |author2-link=Ronald W. Schafer |last3=Buck |first3=John R. |title=Discrete-time signal processing |year=1999 |publisher=Prentice Hall |___location=Upper Saddle River, N.J. |isbn=0-13-754920-2 |edition=2nd |page=55
}}</ref><ref name=ProakisManolakis/>
'''Even symmetry:'''
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'''Even symmetry:'''
A ''N''-point sequence is called ''
:<math>f(n) = f(N-n) \quad \text{for all } n \in \left\{ 1,\ldots,N-1 \right\}.</math>
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'''Odd symmetry:'''
A ''N''-point sequence is called ''
:<math>f(n) = -f(N-n) \quad \text{for all } n \in \left\{1,\ldots,N-1\right\}. </math>
Such a sequence is sometimes called an '''anti-palindromic sequence'''; see also [[Palindromic polynomial|Antipalindromic polynomial]].
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