In Section 2.8, the conjugate-symmetric and conjugate-antisymmetric components of a sequence x[n] were defined, respectively, as
In Section 8.6.4, we found it convenient to define respectively the periodic conjugate symmetric and periodic conjugate-antisymmetric components of a sequence of finite duration N as
(a) Show that xep[n] can be related to xe[n] and that xop[n] can be related to xo[n] by the relations
(b) x[n] is considered to be a sequence of length N, and in general, xe[n] cannot be recovered from xep[n], and xo[n] cannot be recovered from xop[n]. Show that with x[n] considered as a sequence of length N, but with x[n] = 0,n > N/2, xe[n] can be obtained from xep[n], and xo[n] can be obtained from xop[n].
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