[1000mp] Key Clicks -- My MP Experience

[Tom McDermott]

I think this problem isn't really that hard. But I'll give the
complete reasoning. Skip to the summary if pressed for time!


The spectrum of the transmitted CW signal is pretty easy to describe.
It's a continuous carrier modulated by a waveform that turns that
carrier on and off - in other words it's a form of amplitude modulation.

Let's simplify the situation and assume that the continuous CW carrier
is perfectly clean (ignoring phase noise, drift, chirp, etc.) so we
can focus just on the clicks. That carrier is a single spectral line =
with
no width. Let's additionally simplify the problem by assuming that the
CW carrier frequency is really high (MHz) compared to the keying speed=20
(Hz) (a good assumption).

Then, all the spectral width would be due to the amplitude modulation.
Let's assume the worst case - completely hard keying. We'll assume a=20
continuous string of dits. The keying waveform in this case would be a
square wave. 'On' with a perfectly abrupt transition to 'Off' and
then later a perfectly abrupt transition back to 'On'. This is generally
called the 'envelope' of the waveform.

It's obvious the spectrum would be that of a square wave - fundamental
at the keying speed (dits per second) plus all the odd harmonics of that
speed modulating the carrier. Since we are talking amplitude modulation,
we would have an upper and a lower sideband. Thus, spectral lines at
carrier +/- keying rate, carrier +/- 3*keying rate, carrier +/- 5*keying
rate, etc.

What would be the minimum possible width for a CW signal? It would
be a spectrum (at RF) that contained just the +/- keying rate signals, =
and
none of the harmonics of the keying signal. i.e., a spectrum with a
spectral width that is twice the keying rate (remember Nyquist?). And
it would be impossible to utilize such a signal because it wouldn't =
convey
any information. It would just be an AM signal with a sine-wave =
envelope,
i.e. an AM carrier with one constant sinusoidal tone at the keying rate.

Now lets add some useful information to the carrier. We can approximate
the keying waveform of CW as a random keying waveform mixed with our
abrupt on-off envelope. Usually this is called pseudo-random. Although
a real CW signal is not quite so bad, it is a simple way to give us a =
good
approximation of the spectrum. After listening to some operators, =
perhaps
pseudo random would be a perfect approximation  :o)=20

The spectrum of the pseudo-random signal is sin-x/x with the first null
at 1/keying rate, and subsequent nulls at 2/keying rate, 3/keying rate, =
etc.
So the CW signal is going to have maximum energy at the carrier =
frequency,
and then gentle rolloff down to a null in the spectrum at 1/keying rate, =
a
bounce back to -13 db below the carrier (at 1.5/keying rate) back down =
to
zero energy at 2/keying rate, etc., waaaaay on out there.

How do we reduce the spectrum of this signal? Change the envelope to =
soften
the edges. Remember, the spectrum is just the product of the hard square
envelope
with the pseudo-random noise. If we select an envelope with the smallest
spectral width, the CW signal will be minimized in width.

This is a common problem, and it describes what is called a 'window' - a
shaping
function that cleans up the spectrum. These are well known, and the
properties
have been known for a long time. The narrowest possible window is a
raised-cosine
window with an excess bandwidth of zero. You would not want to listen to =
one
of
these, since it has lots and lots of ringing. It has a spectrum out to =
one
half
the baud rate (keying rate). Thus the CW signal, including upper and =
lower
sidebands
would be as wide as 1/keying rate, and would sound awful (much too =
soft).

The widest of the raised cosine windows has an excess bandwidth of 1.0. =
It
has
spectral energy out to the baud rate (twice as wide as the narrowest
possible signal).
The CW signal including upper and lower sidebands would be as wide as
2/keying rate.
It could be useful, but it would still sound extremely 'soft' and no one
would like it.
Increasing the bandwidth of the envelope shaping waveform to allow even =
more
spectrum through (such as four times as wide as necessary) would start =
to
give
A CW signal that does not have clicks but still would be reasonably easy =
to
copy.



Summary: the width of the CW signal is twice the spectrum of the shaped
keying
signal times sin-x/x. The spectrum of the shaped keying signal is the
fourier
transform of that shaping signal. It's easy to determine the spectrum of =
the
shaping signal. If it has any sharp corners, it has a wide (bad) =
response.
The
rise-fall time of the shaping signal determines the energy close in to =
the
carrier,
(within a small value of n/keying rate); at 50 baud, within just a few
hundred hertz.
The sharpness of the shaping edges causes the grief further away.

	-- Tom, N5EG





> What we need to identify are *exactly* which features of the waveshape =

> are causing the wideband clicks. Is it the average rise time, or the=20
> sharpness of the corners... or both? Which features are important, and =

> which don't matter much? Unfortunately that kind of insight needs some =

> high-powered mathematical input.
>
> By coincidence, a ham in Europe who is a DSP expert and a high-powered =

> mathematician has recently started to get interested in this problem.=20
> When there's news, I'll report back.
>
>
> --=20
> 73 from Ian G3SEK         'In Practice' columnist for RadCom (RSGB)
>                             Editor, 'The VHF/UHF DX Book'