(Revised September 1980)
CCWN 77:105



     Wh - v here are two channels. Note that the filter has two channels, each with an Input
Mixer, Integrator, Sample-And-Hold, and Output Mixer.

     If the signal is in phase with the center reference, then the mixer output is always posi-
tive-, the following integrator will see a positive d-c voltage. If the signal is out of phase with
the reference, then the mixer output is always negative; the following integrator will see a nega-
tive voltage. In either case, the filter wo rks normally-, the positive or negative d-c voltage
charges the integrator capacitor; the Sample-And-Hold "remembers" that charge during the foi-
lowing time frame-, and the Output Mixer generates a sidetone whose amplitude is proportional
to the voltage on the Sample-And-Hold capacitor.

     But if the signal is 90 degrees out of phase with the reference frames, then the mixer out-
put will be at times positive and at times negative during a cycle of the input but these will be
averaged to zero by the integrator. The result is zero filter output from this channel.

     This situation is different for the channels because the "Y" channel input mixer is
operated by a reference which is 90 degrees out of phase with the "X" channel's reference.
Thus, if a signal is 90 degrees out of phase with X channel, it will be in phase (or 180 degrees
out of phase) with the Y channel.

     At all phase differences between the two channels the product of the two channels is
alwavs the desired signal, despite the phase relationship between the local reference and the
incoming signal.

     If the desired signal is graphed as a phasor (as in Figure 3) , one might say that the X-
channel picks up the x-component of that phasor, and the Y-channel picks up the y-component
of the phasor.

     The two channels' output mixers are also driven with signals 90 degrees out of phase.
That way, the output tones (regarded as phasors) combine vectorially. The result is that the
combined output is a tone whose amplitude reflects the amplitude of the desired signal, regard-
less of that signal's phase. (Incidently, the phase of the output tone also reflects the phase of
the desired signal.)

     Filter Response Curve. The theoretical response curve of the filter may be developed; we
won't go into the mathematical details here except to say that the amplitude response is a "(sin
x)/x" curve, like that in Figure 4. For a frame length of 0.1 second (10 bit/seconds, or 12
words/minute), the nulls in the filter response occur every 10 Hz either side of the center fre-
quency. The 3-dB points on this curve are 9 Hz apart; the 6-dB points, 12 Hz apart. The
equivalent noise bandwidth" (for signal-to-noise computations) is 10 Hz.

     Figure 5 compares the ccw filter (operating at 0.1 second frames) with an ordinary 500-Hz
cw filter and a 2700-Hz ssb filter. On this scale it is impractical to show the numerous nulls in
the ccw filter response shown instead is the envelop of the primary response.



     How Much Improvement Is Gained In Practice?

     One way of comparing ccw with the ordinary cw method is to consider the filter noise
bandwidth. This is the bandwidth of an ideal steep-sided filter which would pass the same
amount of random noise as the filter being considered. For ccw with a frame length of 0.1
second (10 bits/second, or 12 words/minute), the filter noise bandwidth is 10 Hz. Thus we
should expect about 17 dB superiority over a typical 500 Hz cw filter. Likewise, we would
expect about 23 dB superiority over a 2300-Hz filter. Such estimates should be reasonably
accurate with respect to noise, but when QR,'vl is present the ccw filter probably does better.

     Using a ccw system of 0.1-second frames over ground wave, in the presence of natural
noise, and adjusting power for matching readability, I have measured about 16-dB improvement
over a 470-Hz crystal filter, which is near the theoretically expected value.

     Narrowing the ccw bandwidth - by longer frame times - give additional signal-to-noise
advantage, at the price of slower information transmission rates. A 0.1 second integration
period gives about .6 dB improvement over a 2300-Hz crystal filter. A I-second integration