[Elecraft] CW Bandwidth (was: K3 transmitt filter)

[lyle johnson]

Look at the Tx spectrum plots of radios tested by ARRL. 
 CW signals defintely occupy bandwidth!  If they didn't, 
we could do CW contests in a 10 Hz slice of each band and 
accommodate every Amateur on earth with no QRM!  And have 
essentially 10 Hz left over!

In fact, a CW signal might have no width if you never 
keyed it.  The "C" in CW.  But in fact we turn the carrier 
on and off, and this creates sidebands.  If the signal 
on/off keying is properly shaped, these sidebands will 
occupy little spectrum.  And, if you think about it, the 
total occupied spectrum width will be very nearly the same 
no matter your keying speed up to the limit allowed by the 
"waveshaping."  If the waveshaping, for example, is a 
raised cosine and you key it at a rate such that an 
element just allows the complete waveshaping to occur, you 
will have a 100% modulated AM signal.

So, if the waveshaping were, say, a raised cosine of 5 
msec, and you keyed on for 5 msec, then off for 5 msec, 
then on...  you'd be generating a AM signal 100% modulated 
with a 100 Hz tone.  You occupied bandwidth would then be 
200 Hz.  Thus, to a first approximation, 5 msec 
waveshaping will result in a signal at least 200 Hz wide. 
 As you reduce the keying speed (increase the length of 
the elements, or the "dwell time" for carrier on and 
carrier off, the energy in the sidebands will be reduced 
and the energy in the carrier will be increased.  But the 
signal will still "occupy" 200 Hz of spectrum.

You can get narrow spectrum at these lower keying rates by 
doing more complex waveshaping, but in the extreme (look 
at a sinc function) you'd need to modulate the carrier 
BEFORE the key is closed and for a similar amount of time 
AFTER the key is opened.  This translates to latency, 
since the DSP can't look ahead in time to see what you 
will be doing in the future (if it could, I'd apply THAT 
signal processing algorithm to the stock market!).

We're restricted to filtering that attempts to minimize 
occupied bandwidth while operating with absolute minimum 
delays/latencies.  We CAN apply this sort of waveshaping 
to other digital data modes -- see, for example, James 
Miller, G3RUH, classic article on "The Shape of Bits to 
Come" < 
URL:http://www.amsat.org/amsat/articles/g3ruh/108.html > 
and think about CW rather than PSK while reading it.

We'll never get to zero bandwidth if we want to convey 
information.  I suppose if Shannon hadn't written his 
paper, we'd be able to communicate with zero bandwidth, 
but he did and now we can't... :-)

Enjoy!

73,

Lyle KK7P

> ... a CW signal has no width,