[SOLVED] odd order and even order non-linearity

[iVenky]

I know about non-linearity a little bit.

For example: if we give sinx as input and if the output contains [sin(x)]^2 then obviously we have some other gain for different values of input and at the same time we have some higher frequency components.

Now I recently came across this "even and odd non-linearity".

if the output is o/p voltage= a + bx + cx^2 + d x^3 +....

Then we should not have even-order non-linearity but odd order non-linearity will not cause any trouble. For this to be satisfied I understand that terms like a,c,e.. should be zero.

If this statement is correct then there is no problem if the o/p voltage is = bx + dx^3 +...
How does this odd-order thing solve problem?
I just couldn't understand how odd order is better than the even-order.

Thanks in advance.

 

[crutschow]

I don't understand either.

In an audio system odd order harmonics tend to sound worse than even order harmonics but otherwise they are both distortion and both are undesirable in most systems.

 

[iVenky]

I don't understand either.

In an audio system odd order harmonics tend to sound worse than even order harmonics but otherwise they are both distortion and both are undesirable in most systems.

Yep. That's the reason why I got confused when I came across this thing.

 

[erikl]

A square wave has only odd harmonics

Now I recently came across this "even and odd non-linearity".

if the output is o/p voltage= a + bx + cx^2 + d x^3 +....

Then we should not have even-order non-linearity but odd order non-linearity will not cause any trouble. For this to be satisfied I understand that terms like a,c,e.. should be zero.

If this statement is correct then there is no problem if the o/p voltage is = bx + dx^3 +...
How does this odd-order thing solve problem?

Perhaps you mixed this up with the fact, that a square wave Fourier series shows only odd harmonics. See e.g.:

wiki: Fourier series
fourier series tutorial
**broken link removed**

 

[FvM]

It may be the case, that in special situations odd harmonics are accpetable but even aren't. But you didn't tell any reasons why.

 

[iVenky]

I don't know the reason. That's the reason why I asked this question. I just came across this sentence.

 

[dave9000]

There's a reason for the statement that "odd terms don't matter", but obviously it depends on the contest.
Suppose you are measuring a voltage from DC to 1Hz, and you know that you have a 50Hz interference from the supply line.
If the system if linear it is enough to low-pass filter.
The same if the system is not linear but with only odd order terms.
But the even terms are going to "rectify" your signal (in a sense), disrupting the DC accuray no matter how well you filter.

From another point of view - consider the frequency domain.
A second order term (x*x) becomes a convolution in the frequency domain.
If you make the auto-convolution of the 50Hz signal you get two peaks: one at 0Hz and the other at 100Hz.
The 0Hz peak is the one causing problems.
A third order term is a double-convolution --> peaks at 50Hz and 150Hz --> no problem at DC.

 

[iVenky]

There's a reason for the statement that "odd terms don't matter", but obviously it depends on the contest.
Suppose you are measuring a voltage from DC to 1Hz, and you know that you have a 50Hz interference from the supply line.
If the system if linear it is enough to low-pass filter.
The same if the system is not linear but with only odd order terms.
But the even terms are going to "rectify" your signal (in a sense), disrupting the DC accuray no matter how well you filter.

From another point of view - consider the frequency domain.
A second order term (x*x) becomes a convolution in the frequency domain.
If you make the auto-convolution of the 50Hz signal you get two peaks: one at 0Hz and the other at 100Hz.
The 0Hz peak is the one causing problems.
A third order term is a double-convolution --> peaks at 50Hz and 150Hz --> no problem at DC.

Nice explanation.