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. A sine wave starts out at 0 degree point at
0 amplitude but with a slope of 1. It reaches full amplitude at 90 degrees
phase and here it has zero slope. 90 degrees later, the amplitude is back
to zero, but the slope
is -1. So, I don't follow the argument. For clickless operation, we must
start and stop at zero slope. A sine or cosine wave does not do this.
Carl Moreschi N4PY
----- Original Message -----
From: "George, W5YR" <email@example.com>
Sent: Wednesday, February 06, 2002 4:15 PM
Subject: [TenTec] More on Keying Waveshapes (long)
> At Tom Rausch's suggestion, I am posting the following results of
> 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
> 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
> 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
> 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
> 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
> 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
> filtering and limited or no waveshaping of the received code elements -
> a lot to do with the keying artifacts we observe.
> PSK31 Modulation Theory
> Peter Martinez G3PLX
> The 31 baud BPSK modulation system used in PSK31 was introduced by SP9VRC
> his SLOWBPSK program written for the Motorola DSP56002EVM. Instead of the
> traditional frequency-shift keying, the information is transmitted by
> of polarity-reversals (sometimes called 180-degree phase shifts)This
> can be thought of as equivalent to sending information by swapping-over
> wires to the antenna, although, of course, the keying is more usually done
> in the audio input into the transceiver. A well-designed PSK system will
> better results than the conventional FSK systems that amateurs have been
> for years, and is potentially capable of operation in much narrower
> than FSK. The 31 baud data rate was chosen so that the system will just
> hand-sent typed text easily.
> There is a problem with PSK keying which doesn't show up with FSK, and
> 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
> gate, at 31 baud, the emission would be extremely broad. In fact it would
> about 3 times the baudrate wide at 10dB down, 5 times at 14dB down, 7
> 17dB down, and so on (the squarewave Fourier series in fact).
> The solution is to filter the output, or to shape the envelope amplitude
> each bit which amounts to the same thing. In PSK31, a cosine shape is
> 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
> test signal, it IS a two-tone test signal, and the spectrum consists of
> 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
> 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
> 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
> "hard-keying" on the receive side is a BPSK receiver which opens a gate at
> start of a bit, collects and stores all the received signal and noise
> the bit, and then "snaps" the gate shut at the end. This process gives
> the receive-side equivalent of key-clicks, namely sidelobes on the
> passband. So, although this "integrate-and-dump" method is 100% efficient
> the task of sorting out signal from noise, it will only reject signals by
> at 3 times the baudrate wide and so on, the same spurious rejection
> that we got as spurious emission figures for the transmit side. The PSK31
> receiver overcomes this by filtering the receive signal, or by what
> the same thing, shaping the envelope of the received bit. The shape is
> complex than the cosine shape used in the transmitter: if we used a cosine
> the receiver we end up with some signal from one received bit "spreading"
> 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
> 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
> +/-31Hz and beyond, and doesn't introduce any inter-symbol-interference
> receiving a cosine-shaped transmission.
> Note that the transmitter and receiver filters have to be "matched" to
> 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
> someone else came along wanting to improve the performance, they would
> get everyone else to change their transmit filters. I have therefore
> use the simple cosine shape for the transmitter and match that in the
> This leaves the way open for others to develope better receivers without
> transmitters being incompatible with old. This is slightly different from
> SP9VRC approach.
> 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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