OOPS!

On Wed, 21 Apr 1999, Robert Macy wrote:

> Can't make a general statement.  A  "perfect" square wave of 50% duty
> cycle is missing all the even harmonics.  A "perfect" 25% duty cycle is
> missing every harmonic that's a multiple of 4 with even harmonics higher
                                                     ^^^^
should have read....odd

> than odd harmonics.  As you "slide" between 25% and 50%, harmonics come
> and go with some odd higher and some even higher, depends.  
> 
> To see the effect draw a sinx/x waveform.  Then every zero crossing call
> that an odd harmonic and every maximum is an even harmonic for a 50%
> square wave.  Mark all the potential harmonics you have as dots along the
> axis.  
> 
> Assume you change to 25% duty cycle, that's like having higher frequency
> content, but still with the basic sinx/x.  Since you changed the width of
> the pulse in half the frequency spectrum (which was sinx/x) moves out 2:1.  
> 
> That just means the gentle slope of your sinx/x now crosses at the 4th
> harmonic instead of the 2nd harmonic.  As you draw the little spikes of
> energy, you'll see you have 2nd, 3rd, no 4th, 5th, 6th, 7th, no 8th, etc.  
> 


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