# even and odd signals

Discussion in 'Electronics Homework Help' started by bhuvanesh, Feb 17, 2015.

1. ### bhuvanesh

201
0
Aug 29, 2013
Signals can be in nature or we artificially produce it. In nature no signals are going to be in even or odd. so other option we have is to produce.So my next question is why we want to produce such signal(even and odd signal) ?

content form my signal book by oppenheim
why we need to do even-odd decomposition for the signal.what is the use in that ?

Thank you in advance

2. ### Merlin3189

250
69
Aug 4, 2011
Without more context I can't think of much to say about odd and even functions.
The distinction seems to be largely one of how you can treat them in various mathematical tricks - whether you can integrate from -infinity to + infinity in one go, or whether you need to do it in two halves, for eg.

I really don't know if there is some deep general significance to whether a function is odd or even. The issue just crops up sometimes when doing the maths.

I'd probably get in trouble with people like LvW for saying it, but I don't think maths is reality. It's all just models and often very imperfect models. The maths model has to take account of the real world, but the real world does not necessarily have to take account of the maths. Sometimes maths reveals some insight into the world that we did not have before, but sometimes things that crop up are just artefacts or quirks or imperfections in the models. In maths we do some pretty incredible things - pulses that last for zero time, have finite size but stil have power; signals that exist from - inf to + inf ; signals that instantaneously change from one value to another. None of these seem physically plausible, but doing maths with them can give useful results. It's hardly surprising that they sometimes give impossible results or require us to do other weird things to make them work.

I just don't worry about it. If it reliably gives us the useful results we need, use it. If it seems to suggest something weird, well, think about it a bit in case it is important, but if it's just weird, ignore it.

bhuvanesh likes this.
3. ### Harald KappModeratorModerator

11,955
2,793
Nov 17, 2011
Even: x(-t) = x(t)
Odd: x(-t) = -x(t)

This kind of signals is used in the decomposition of complex periodic signals into a sum of simple periodic signals (constituent signals). One example is the Fourier transform. Here a periodic signal is represented by the sum of periodic sine (odd) and/or cosine (even) functions.
The use of transforming signals is that it is sometimes much easier to analyze or work with a transformed signal than to use the original signal.

bhuvanesh likes this.
4. ### bhuvanesh

201
0
Aug 29, 2013
ohhh separating the components makes work easier
Thank you