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10.20 expandConjugateEven() and expandConjugateOdd()

PrototypesHeader Files
RWMathVec<DComplex>
expandConjugateEven(const
RWMathVec<DComplex>&)
<rw/math/mathvec.h>
RWMathVec<DComplex>
expandConjugateOdd(const
RWMathVec<DComplex>&)
<rw/math/mathvec.h>

10.20.1 Description

Given a complex sequence C(n), n=0, ..., 2N points long, it is a complex conjugate-even sequence if:

C(n) = conj[C(-n)] = conj[C(2N-n)],

and a complex conjugate-odd sequence if:

C(n) = - conj[C(-n)] = - conj[C(2N-n)].

Note that for a sequence to be complex conjugate-even, the imaginary parts of C(0) and C(N) must be 0, and for a sequence to be complex conjugate-odd, the real parts of C(0) and C(N) must be 0. Given the lower half of the sequence, that is, C(n), n=0, ..., N, these functions expand it out to the entire sequence C(n), n=0, ..., 2N.


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