- #1
dervast
- 133
- 1
Hi i am stuck with something really simple :(
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
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