> I'm a little confused over the cosine shape as you have descibed it.
> The zero slope points on a cosine curve (or sine curve) are 180
> degrees apart and not 90 degrees apart.
That's why it is called a raised-sine in this application, since it
starts and stops at zero slope.
The key to all of this is bandwidth.
Assume we start with a square wave from a key and we filter it in a
low pass filter so the harmonics of the rise and fall are limited in
bandwidth. We set the cutoff frequency of the filter so at the
highest expected keying rate the filter passes just beyond the third
The result is a filtered waveform that is plenty hard yet does not
contain any unnecessary harmonics. If we set the total transition
time to about 5mS we will have, when considering bandwidth of
filters, a virtually clickless signal without being "soft" at all speeds
virtually all of us can work with.
My radio has a similar waveshape, and it passes 60 WPM dots
with reasonable quality. I can still use a tuning pulser with 70WPM
dots and 20% weight to adjust the amplifier to full PEP power.
I think what has happened is our computers, sidetones, and radios
are so clicky that we think the clicks are somehow meaningful,
acceptable, or necessary.
73, Tom W8JI