Register to reply

Even and odd signals

by dervast
Tags: signals
Share this thread:
Apr18-07, 07:14 AM
P: 133
Hi i am stuck with something really simple :(
I know that we can express a signal with the even and odd signal
(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
Phys.Org News Partner Engineering news on
Catching grease to cut grill pollution
Researchers develop tool to predict the level of driver discomfort caused by LED lighting
New inexpensive and easy to implement computer software provides real-time and highly accurate data on traffic
Apr18-07, 07:27 AM
P: n/a
Why would you consider equations 1 and 2 at all? A generic function x(t) will not have those properties always. The only function for which both of those equations can be true is x(t) = 0, which is consistent with your result x(t) = 4x(t).
Apr18-07, 12:42 PM
P: 133
I cant understand what u are saying me . Plz try to clarify where i am wrong.
Thx a lot

Apr18-07, 04:45 PM
P: n/a
Even and odd signals

Ok here is what makes your thinking wrong: You try to use x(-t) = x(t) and x(-t) = -x(t), two VERY SPECIFIC conditions, to show something for any x(t) which could have any sort of shape. What you meant to use for equations 1 and 2 was:

xe(-t) = xe(t) (1)
xo(-t) = -xo(t) (2)

If you assume equations 1 and 2 are true then you are implying x(t) = 0 for all t

I hope I made myself more understandable.
Apr19-07, 01:06 AM
P: 133
Yes thx a lot i have clearly understand my wrong. But if someone ask me to prove that
xe(t)=1/2[x(t)+x(-t)] how shouldi think to prove that?
Apr19-07, 10:20 AM
P: n/a
I would use the definition of an even function xe(t) = xe(-t), but recall that xe(t) = 1/2[x(t) + x(-t)], so what would xe(-t) be?

Register to reply

Related Discussions
Rz vs nrz signals Electrical Engineering 6
Signals and systems - is this right? Electrical Engineering 14
Help with Signals and ICA Electrical Engineering 2
Energy Signals Introductory Physics Homework 1
Matching partial signals to whole signals Electrical Engineering 0