Harmonics question

[Don Tillman]

   From: Magnus Danielson <magnus at analogue.org>
   Date: Tue, 19 May 1998 23:59:25 +0200

   Gene missed one term, the DC term which may also exist. 
   Being a bit overprecise I would say that you can view a periodic
   waveform as being built up by a number of sines and a DC term. 

DC is just the zeroth harmonic.  (Phase shifted, make it a cosine
wave.) 

   Date: Tue, 19 May 1998 15:08:15 -0700 (PDT)
   From: Sean Costello <costello at costello.seanet.com>

   I may be wrong at this, but I recall reading that if the top and
   bottom of a waveform are mirror images of each other (i.e. if you
   lined up the positive section of the waveform with the negative
   excursions of the waveform), then the signal contains only odd
   harmonics.

'Depends on how you hold the mirror.  If you say it just a little more
precisely...

If the second half of the waveform is exactly the same as the first
half of the waveform, but upside down (inverted negative/postive),
you've got yourself a waveform with no even harmonics.  Interestingly
this will hold no matter where you decide you'd like the waveform to
start.  

Ie, given a waveform F(t) of period T, you'll have no even harmonics
if F(t+T/2)=-F(t).

   Is there any simple function that contains all even harmonics?  If
   so, what does the waveform look like?

Any waveform with the second half exactly the same as the first half,
not inverted as above, will have all even harmonics, including no
fundamental.  But that's just a waveform at double the frequency.

  -- Don