09-05-2014, 10:47 AM
ODD AND EVEN SYMMETRY PROPERTIES OF DFT
AIM
To verify the symmetry property of odd and even sequences in 1D-DFT.
THEORY
A real number sequence can be decomposed into odd and even sequence, symmetry property of these sequence is given by
DFT[ xec(n) ] = Re[ X(k) ] = Re[ X((-k))N ]
DFT[ xoc(n) ] = Im[ X(k) ] = -Im[ X((-k))N ]
Where xec(n) = 0.5[ x(n) + x((-n))N ] ; xoc(n) = 0.5[ x(n) - x((-n))N ] are the even and odd sequence of signal x(n).