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even and odd symmetry

A signal is even (symmetric) when $x[-n]=x[n]$ , and odd (antisymmetric) when $x[-n]=-x[n]$ .

A sequence is even (symmetric) when $x[-n]=x[n]$ -- a mirror image of itself around $n=0$ -- and odd (antisymmetric) when $x[-n]=-x[n]$ , flipped in sign as well as reflected. Every signal decomposes uniquely into an even part plus an odd part.

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