[Elecraft] K3 CW rise time mod - Definition

[Lyle Johnson]

> ...Worse, the latest handbook Figure 9.8 states that on-off 
> transitions of the RF envelope should follow  a sine-wave curve, so I 
> don't quite know what to make of "DSP-generated raised-cosine key 
> shaping." 

Let me see if I can shed a glimmer of light here.

A sine wave, going from 0 to 360 degrees (or 0 to 2 pi radians if you 
are of at persuasion), starts at 0, then builds to +1 at 90 degrees 
(pi/2 radians), dropping down to 0 again at 180 degrees (pi radians), 
then further dropping to -1 at 270 degrees (3 pi/2 radians) returning to 
0 at 360 degrees (2 pi radians).

OK, I'll stop the radians now :-)

I suggest you sketch this on a sheet of paper to make it easier to 
follow along.

A cosine is shifted by 90 degrees, starting at -1 for 0 degrees, 
building to +1 at 180 degrees, and dropping again to -1 at 360 degrees.

The shape is the same.  The cosine starts at its minimum value (-1) at 0 
degrees while a sine wave is already halfway between its minimum (-1) 
and its maximum (+1) at 0 degrees.

Our RF power can't go negative in the real world, so if we want to shape 
our keying, we must go from 0 to some positive value.

One way to do this is to add 1 to the sine or cosine value.

If we do this, the cosine goes from 0 at 0 degrees, to +2 at 180 
degrees, then drops back to 0 at 360 degrees.  The sine does the same, 
just offset.

Adding 1 to the value makes it a "raised cosine" (or a "raised sine, if 
you want to talk about sines -- the wave *shape* is identical).

Thus, "raised cosine shaping" and "follows a sine-wave curve" are two 
ways of saying essentially the same thing.

Now, the reason we usually talk about a raised cosine is because we (or 
at least, I) like to start a wave generator at 0 degrees, and a cosine 
is conveniently at its lowest value at 0 degrees.

Thus, to shape the CW waveform, the DSP starts a cosine generator at 0 
and applies the result, offset by adding 1, to the RF envelope it is 
creating.  AT 180 degrees, it stops. The RF waveform is at its maximum 
amplitude, the wave is properly shaped, and your adjacent channel 
neighbors are happy (or as happy as they're going to be!).

The DSP can make this transition time be 5 ms - or 500 microseconds, or 
10 seconds, or whatever it sis told to create.

If you want to get a good visual look at all this, I highly recommend 
the paper by James Miller entitled "The Shape of Bits to Come." < 
URL:http://www.amsat.org/amsat/articles/g3ruh/108.html > If you read it, 
forget about PSK or FSK, and think about CW waveshaping.  Also, remember 
that CW is traditionally decoded by ear, so any waveshape that requires 
you to look ahead in time (like the really narrow spectra he describes) 
would probably sound very odd by ear and would require that the dits and 
dahs being sent be delayed by 4 or 5 dot times.

But it would make you a very good neighbor!

73,

Lyle KK7P