On Fri, 26 Feb 2021 01:57:59 -0800 (PST), "
wrote:
** You sure about "any" ?
Square waves have cascading, odd numbered harmonics.
The ringing one would merely be out of step with the others.
Ringing and how it works was brought home to me when I had to set up a
CNC mill. Part of the setup was automatic, and was for the movement
servos to characterize themselves. When they come to a fast stop, the
heavy stuff attached rings (wobbles), and that has to be prevented. So
the servos use feedback to find the frequency of that ring. Then they
use a convolution algorithm to notch that frequency out of the
transient edge. Result - fast stops and no ringing or oscillation.
In linear systems frequencies can't be created out of nothing. All
frequencies are present in a fast edge, and this is where the energy
for the ring comes from. Remove that frequency from the edge and you
will not see any ringing. Note - this is not the same as harmonics of
the square wave. It is a continuous sinc curve of energy associated
with each edge.
This is super non-intuitive but provided there is no non-linearity, it
works.
d
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