M 5.3 Using MATLAB, verify the symmetry relations of the DFT of a complex sequence as listed in Table 5.1. Table 5.1: Symmetry properties of the DFT of a complex sequence. Length-N Sequence N-point DFT x[n] = xre[n]+jxim[n] = X[k] Xrelk]+jXim[k] x*[n] x*[(-n)N] X*(-k) N X*[k] Xre[n] Xes[k] = (X[k]+x*((-k)N]} jxim Xes[n] Xcalk]=(X[k]-X*[(-k)N]} Xre[k] Xca[n] jXim[k] Note: Xes[n] and xca[n] are the circular conjugate-symmetric and cir- cular conjugate-antisymmetric parts of x[n], respectively. Likewise, Xes[k] and Xca[k] are the circular conjugate-symmetric and circular conjugate-antisymmetric parts of X[k], respectively.