The question to be answered is whether a few stronger tones or many weaker tones provide a better signal to use for automatically starting and stopping a recording
A 3-tone signal was used for the "few stronger tones" case. The 12-tone signal produced by the leader and trailer was used for the "many weaker tones" case.
Both of these signals were subjected to simulated 2-path conditions selected to significantly attenuate one of the tones and to also provide some attenuation of a second tone.
The red trace below shows the level and the frequencies of the uncorrupted 3-tones of one of the 3-tone test signals.
The affects on the amplitude of this signal for the selected 2-path conditions are shown by the black trace.
The black trace shows that: the tone just above 1800 Hz has been attenuated by about 27 db, the tone near 1600 Hz has been attenuated by less than 2 db, and the tone just below 1200 Hz has been attenuated by about 13 db.
The red trace below shows the level and the frequencies of the uncorrupted 12-tones from the trailer test signal. Note that the uncorrupted levels are about 3 db lower than for the case of the 3-tone signal.
The affects on the amplitude of this signal for the selected 2-path conditions are shown by the black trace.
The black trace shows that: the tone just below 1800 Hz has been attenuated by about 27 db, the tone just above 1200 Hz has been attenuated by about 13 db, the tone near 800 Hz has been attenuated by about 10 db, the tone just below 2200 Hz has been attenuated by about 6 db, and the tone just above 1500 Hz has not been attenuated.
There are two significant points to notice in the following plot. First, near 155 on the horizontal scale, the cross-correlation is a little over 0.7. This is during the time when the "3-tone signal" should be detected.
Second, near 120 on the horizontal scale, the cross-correlation value is near 0.6. This is at a time when the "3-tone signal" should NOT be detected.
Note that for the "12-tone leader" signal, the cross-correlation value is just over 0.8, near 145 on the horizontal axis.
Since the same "12-tone" signal was used for the leader, and the simulated 2-path conditions (which changed with time) did not corrupt the leader as badly as they did the trailer, the cross-correlation value is just under 0.9 near 25 on the horizontal scale.
At times when it should NOT be detected, the cross-correlation value for the 12-tone signal was well below 0.5.
Thus, for a similar amount of corruption, the cross-correlation value for the 12-tone signal was greater where it should be detected and smaller where it should NOT be detected, than was the cross-correlation value for the 3-tone signal. The 12-tone signal would therefore be expected to provide a more reliable signal that the 3-tone signal, in the presence of multipath.
What I have called "cross-correlation" is called "correlation coefficient" in statistics text books. Following is the formula used to calculate this value.
There is another criterion required of signals to be used to automatically start and stop a recording. That criterion is that the signals should be relatively uncorrelated with the portion of the signal representing the data being transferred.
Unfortunately, as shown in the plot below, the 12-tone "leader/trailer" signal shows cross-correlation values near 0.6 over significant portions of the data section for a file generated by KB4YZ.
Thus, something other than the 12-tone leader/trailer signal is needed for use in automatically starting and stopping a recording.
The following plot was generated from a data file containing runs of all 256 possible 8-bit patterns. Each of the 256 patterns was repeated, such that there were a total of 44 instances of each pattern.
As the cross-correlation value near 0.7, at about 700 on the horizontal scale shows, there is a case even worse that the one demonstrated by the file generated by KB4YZ.
Below is the spectrum of a 10-tone signal that should be able to serve as both a leader, and as a signal to automatically start a recording.
This proposed new leader is currently being transmitted just prior to the old 12-tone leader.
Below is the spectrum of a 10-tone signal that should be able to serve as both a trailer, and as a signal to automatically stop a recording.
This proposed new trailer is currently being transmitted just after to the old 12-tone trailer.
The next two plots show that the cross-correlation of the proposed new leader and trailer against the data file created by KB4YZ is comfortably below 0.5
The next two plots show the cross-correlation of the proposed new leader and proposed new trailer signals against the data file containing runs of each of the 256 possible 8-bit patterns.
The greatest undesirable cross-correlation of the proposed new leader is about 0.54.
The greatest undesirable cross-correlation of the proposed new trailer is about 0.58.
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