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[Supply current of 3 phase semi converter]

![enter image description here

I've been told that shifting this waveform left by 30 + a/2 will make it odd. Odd means f(a) = -f(a), right? So, how it that happening here?

Or am i missing something? Signal shown is the supply current waveform of a 3 phase semi controlled rectifier.

colormegone
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Vivek Subramanian
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1 Answers1

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Function $f$ is said to be even if $f(-x)=f(x)$ for all such $x$ that both sides of equality are defined. From graphic point of view even functions are symmetric about the y-axis.

Function $f$ is said to be odd if $f(-x)=-f(x)$ for all such $x$ that both sides of equality are defined.

Now let $f$ be the function from your sketch (with 3 humps). Obviously it's neither odd nor even. But if we consider function $g$ obtained from $f$ by left shift to meet the following plot:

![plot

we'll see that $g$ is even. As you may observe, there's no such shift that would make function $f$ odd. However by some shifts you can obtain such function $h$ that its restriction to an interval $(-a,a)$ for some $a$ would be odd. The most meaningful ways to do this are like this

![plot or like this ![plot

Pink background indicates the chosen interval.

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Glinka
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  • But, that depends on what your defining as interval, right? it's even about the origin, but from origin to half of the negative hump, won't it be odd? – Vivek Subramanian Jul 09 '16 at 03:44
  • @VivekSubramanian, yes, but evenness or oddness is always considered "about the origin" (if I understood you correctly), see definition. However some shifts can make your function "locally" odd. – Glinka Jul 09 '16 at 13:04