At Tom Rausch's suggestion, I am posting the following results of examining
the CW ID keying waveform of a popular PSK31 program (MixW) by scope to
determine the rise and fall times and to examine the shape of the on and
off transitions from zero to full power and vice versa.
The particular keying waveshape (a cosine) that is used results
theoretically in all keying transients being confined to within the
bandwidth of the PSK31 signal: 31.25 Hz. Listening critically to this
keying reveals no discernible keying artifacts other than the simple keyed
tone.
Compared to normal CW keying practices, the rise and fall times of 20 msec
each give the keyed signal a very soft characteristic which, although
copiable at 15 wpm, becomes almost a blur at 30-35 wpm due to the lack of
delimiting space between the code elements.
But it is not the long transition times that account for a lack of clicks.
Rather it is the detailed shape of the switching function. A cosine
waveform starts at zero and in 90 deg achieves a maximum value. At the
begining the slope of the waveform (first derivative) is zero, as it is
again at the conclusion. Thus with the cosine keying waveform the entire
transition, from zero to maximum and from zero slope to zero slope, is made
with no discontinuities.
I think that the message can be summed up by saying that as long as the
keying transitions are smooth with no discontinuities in the keyed
waveform, then the length of time required for the transition is a
secondary consideration. Excessively long transitions do not avoid clicks
and other artifacts if they are implemented such that there are abrupt
changes in the keyed waveform. Such long times just make the code hard to
read.
The more convenional RC exponential keying waveform looks superficially
like the cosine function, but although it starts with a zero slope it
reaches it endpoint - full output power - with a non-zero slope and a large
discontinuity occurs at that point. And that is what generates the click,
however long or short the transition.
Conclusion: the reason PSK31 CW ID keying does not present clicks is the
shape of the transition, not its duration. We can use this approach to
avoid artifacts in conventional CW keying. In particular this can help us
to understand that merely using long rise and fall times does not in itself
assure us of clickless keying.
I hope that I will be forgiven the use of the bandwidth, but I have
attached the following excerpt from Peter (G3PLX) Martinez's Help file in
his original PSK31 program. In it he gives a very good explanation as to
his choice of keying waveshape for PSK31 and its influence on keying
artifacts outside the bandwidth of the PSK31 signal itself. In particular,
he suggests that the conventional design of our receivers - simple passband
filtering and limited or no waveshaping of the received code elements - has
a lot to do with the keying artifacts we observe.
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PSK31 Modulation Theory
by
Peter Martinez G3PLX
The 31 baud BPSK modulation system used in PSK31 was introduced by SP9VRC
in
his SLOWBPSK program written for the Motorola DSP56002EVM. Instead of the
traditional frequency-shift keying, the information is transmitted by
patterns
of polarity-reversals (sometimes called 180-degree phase shifts)This
process
can be thought of as equivalent to sending information by swapping-over the
two
wires to the antenna, although, of course, the keying is more usually done
back
in the audio input into the transceiver. A well-designed PSK system will
give
better results than the conventional FSK systems that amateurs have been
using
for years, and is potentially capable of operation in much narrower
bandwidths
than FSK. The 31 baud data rate was chosen so that the system will just
handle
hand-sent typed text easily.
There is a problem with PSK keying which doesn't show up with FSK, and that
is the effect of key-clicks. We can get away with hard FSK keying at
moderate baudrates without generating too much splatter, but polarity
reversals are equivalent to simultaneous switching-off of one transmitter
and switching-on of another one in antiphase: the result being keyclicks
that are TWICE AS BAD as on-off keying, all other things being equal.
So if we use computer logic to key a BPSK modulator such as an exclusive-or
gate, at 31 baud, the emission would be extremely broad. In fact it would
be
about 3 times the baudrate wide at 10dB down, 5 times at 14dB down, 7 times
at
17dB down, and so on (the squarewave Fourier series in fact).
The solution is to filter the output, or to shape the envelope amplitude of
each bit which amounts to the same thing. In PSK31, a cosine shape is used.
To see what this does to the waveform and the spectrum, consider
transmitting a sequence of continuous polarity-reversals at 31 baud. With
cosine shaping, the envelope ends up
looking like full-wave rectified 31Hz AC. This not only looks like a
two-tone
test signal, it IS a two-tone test signal, and the spectrum consists of two
pure tones at +/-15Hz from the centre, and no splatter.
Like the two-tone and unlike FSK, however, if we pass this through a
transmitter, we get intermodulation products if it is not linear, so we DO
need to be careful not
to overdrive the audio. However, even the worst linears will give
third-order
products of 25dB at +/-47Hz (3 times the baudrate wide) and fifth-order
products of 35dB at +/-78Hz (5 times the baudrate wide), a considerable
improvement over the hard-keying case. If we infinitely overdrive the
linear,
we are back to the same levels as the hard-keyed system.
There is a similar line of reasoning on the receive side. The equivalent to
"hard-keying" on the receive side is a BPSK receiver which opens a gate at
the
start of a bit, collects and stores all the received signal and noise
during
the bit, and then "snaps" the gate shut at the end. This process gives rise
to
the receive-side equivalent of key-clicks, namely sidelobes on the receiver
passband. So, although this "integrate-and-dump" method is 100% efficient
in
the task of sorting out signal from noise, it will only reject signals by
10dB
at 3 times the baudrate wide and so on, the same spurious rejection figures
that we got as spurious emission figures for the transmit side. The PSK31
receiver overcomes this by filtering the receive signal, or by what amounts
to
the same thing, shaping the envelope of the received bit. The shape is more
complex than the cosine shape used in the transmitter: if we used a cosine
in
the receiver we end up with some signal from one received bit "spreading"
into
the next bit, an inevitable result of cascading two filters which are each
already "spread" by one bit. The more complex shape in the receiver
overcomes
this by shaping 4 bits at a time and compensating for this intersymbol
interference, but the end result is a passband that is at least 64dB down
at
+/-31Hz and beyond, and doesn't introduce any inter-symbol-interference
when
receiving a cosine-shaped transmission.
Note that the transmitter and receiver filters have to be "matched" to each
other for the ISI performance to be right. Some systems like this use a
pair of
identical receive and transmit filters which are matched. If I did this and
someone else came along wanting to improve the performance, they would have
to
get everyone else to change their transmit filters. I have therefore chosen
to
use the simple cosine shape for the transmitter and match that in the
receiver.
This leaves the way open for others to develope better receivers without
new
transmitters being incompatible with old. This is slightly different from
the
SP9VRC approach.
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72/73/oo, George W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13qe
Amateur Radio W5YR, in the 56th year and it just keeps getting better!
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