Hi i am stuck with something really simple :((adsbygoogle = window.adsbygoogle || []).push({});

I know that we can express a signal with the even and odd signal

x(t)=xe(t)+xo(t)

(xe(t) means even signal and xo(t) means odd signal)

x(-t)=x(t) for even signals and (1)

x(-t)=-x(t) for odd signals (2)

where even signal is

xe(t)=1/2[x(t)+x(-t)] (3) and the odd one is

xo(t)=1/2[x(t)-x(-t)] (4)

i can validate that x(t)=xe(t)+xo(t) if i use equations 3 and 4

x(t)=1/2[x(t)+x(-t)]+1/2[x(t)-x(-t)]= 1/2x(t)+1/2x(t)+1/2x(-t)-1/2x(-t)= x(t) done

My problem arise when i try to use (1)+(2) to (3)+(4) to prove what i want

using (1) to (3) we have xe(t)=1/2[x(t)+x(t)] =2/2x(t)

using (2) to (4) we have xo(t)=1/2[x(t)-(-x(t))] =2/2x(t) and that means that i have proved that x(t)=4x(t)

P.S Plz tell me where i am wrond and correct my bad english mathematical phrases

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# Even and odd signals

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