IV. CROSS-TALK ANALYSIS
Figures [3, 4 and 5] are plots of spectra of two channels for the three phrases in question (we have deposited data on magnetic tape for these and other spectra referred to in this paper with the National Academy of Sciences Archives). In these figures, the spectra for the two channels are placed side by side, on the same time/frequency scale, and are time aligned. The horizontal scale is in seconds but actual numbers have no significance; they are only for reference purpose. Figures 4 and 5 have a common time origin. Note that the time scale on Figure 5 is compressed by a factor of 2 to accommodate a longer duration on this segment. On Figure 4, the time difference between two channels is 4.38 seconds. On Figure 5, the time difference is 7.15 seconds, indicating that the Channel-II recorder had stopped for (7.15 - 4.38) = 2.77 seconds. The vertical scale is frequency in kHz. As mentioned earlier, a spectrum is computed every 10 ms with 50-Hz resolution. Each of these value is plotted, if it is above a certain threshold, with a grey dB-scale for each plot. Values above a second threshold give completely black area. The grey scales also indicate the two thresholds for each plot. The frequency range is restricted to 4 kHz.
On Channel-I spectra, several narrow-band high-energy tones are intermittently present for short durations. These tones are not on Channel II. Also at the end of each tone. there is evident a sharp drop in total Channel-I energy. This indicates some kind of AGC (Automatic Gain Control) action.
These narrow-band tones are called heterodynes. They were generated when another transmitter came on the radio channel, while the transmitter with the stuck-open mike was transmitting. The difference in their carrier frequencies resulted in the heterodynes. If the second carrier is strong. it should also activate the AGC action in the IF (Intermediate Frequency) stage of the radio receiver. The following table lists all the heterodynes on Channel I for the spectra segments shown in Figures [3(a), 4(a) and 5(a)].
Table 2. Channel-I Heterodynes. Figure Heterodyne Timings Seconds 3(a) 9.52 - 9.64 3(a) 10.78 - 10.93 4(a) 7.91 - 8.83 5(a) 20.17 - 21.23 5(a) 22.41 - 22.49* 5(a) 25.81 - 26.30
*Note this heterodyne is around 1200 Hz.
Most radio receivers have an AGC circuit at IF stage to maintain a steady IF signal level at the detector or discriminator. If there is a sudden increase in the RF signal (such as caused by switching on a strong carrier). AGC acts rapidly to reduce the IF amplifier gain to bring down the signal within acceptable limits. On the other hand if there is sudden decrease (such as caused by switching off a strong carrier) in the RF signal level, AGC acts more slowly to restore the IF amplifier gain. This is a typical characteristics [sic] of an AGC circuit: fast attenuation and slow recovery. The AGC action also affects the audio output level because of the drop in overall gain of the system. Therefore, when a heterodyne begins, we should expect a sudden drop in the recorded level of the signal picked up by the stuck-open mike. And after the heterodyne ends, we should expect a slow recovery in the audio signal to its original level. This phenomenon is indeed observed in Channel-I spectra.
If the Channel-II cross-talk was indeed picked up by the stuck-open mike, its level should change to reflect Channel-I receiver AGC action. To test this hypothesis, we estimate the level of cross-talk as a function of time and compare with timing of Channel-I heterodynes. Before we look at it quantitatively, let us examine the spectra again.
On Channel-II spectra (Figs. [3, 4 and 5]) we note that during voice transmissions there are no silence gaps between words. The signal level of Channel II is fairly constant. This could result from the presence of nearby motorcycle radios tuned to Channel II, while someone is transmitting on Channel II. A radio receiver close to a transmitting mike could form a closed loop having greater than unity gain. This will excite a natural frequency of the loop and it will act as an oscillator. The resulting oscillations will be recorded on the Channel-II recorder. We notice this phenomenon on Channel-II recording. During these periods, the spectra consist of a strong sinusoid (in the frequency range 1300-1800 Hz) and its harmonics. There is virtually no other signal present during these periods. We call these "Brieftones." Being high energy and very narrow-band, these are extremely valuable in determining the cross-talk level. On Channel II spectra (in Figures 4(b) and 5(b)) I second harmonics of brieftones are quite prominent, while on Channel I spectra, all the Channel-II brieftones are present but their harmonics are not visible, indicating the limited frequency range of Channel I (even in the normal recording of Channel-I communications, the Channel-I recording has a similar roll-off at high frequencies.).
Estimation of the Cross-talk Level
We can model Channel-I power spectra as follows:
S1(t,f) = S2(t,f)·F(f) + N(t,f)
S1(t,f) is Channel-I spectra at time t,
S2(t,f) is Channel-II spectra at time t,
N(t,f) is spectra of additional Channel-I noise, heterodyne, etc.,
F(f) is the frequency transfer function from Channel-II to Channel-I, and
T(t) is the time-varying cross-talk level.
Our main interest is in estimating the T(t) function. As mentioned earlier, we obtain best estimates of T(t) from those time-frequency bins where Channel-II brieftones are present. In these bins, the Channel-II energy density is very high and therefore it is expected that N(t,f) term in the above equation would be small compared to the contribution from Channel II. This assumption may break down if T(t) is small. In any case this analysis gives an upper bound on T(t). Actual T(t) may be smaller reflecting the contribution from N(t,f) term. Since brieftones are confined to a narrow frequency range (typically two or three frequency bins), we can assume that F(f) is constant over this frequency range. Then, T(t) can be estimated from those time frames where a brief tone is present as
T(t) = Σ S1(t,f)/Σ S2(t,f)
where the summation is carried out only over the brief tone frequency bins.
T(t) is plotted in Figures [6, 7 and 8 where total Channel I and II energy are also plotted. In these figures, the bottom scale is Channel-II time (same as in Figures [3(b), 4(b) and 5(b)]), the top scale is Channel-I time (same as in Figures [3(a), 4(a) and 5(a)]), the left scale is for T(t) in dB, and the right scale is for total channel energy in dB. Channel-II energy is plotted as a solid line, Channel-I energy is plotted as a broken line, and the triangles represent T(t), which are plotted only for those frames where a Channel-II brief tone is present. Channel-I heterodynes are also marked on these plots.
Now we discuss implications of these plots. We shall begin with the "Pre-Stemmons" phrase (Figure 7). During this phrase, T(t) is generally increasing reaching a value of about 7 dB before the Channel-I heterodyne begins at 7.91 seconds (Channel-I time). For the next Channel-II brieftone (from 3.90 to 4.16 seconds, Channel-II time), T(t) is around -10 dB; a drop of 17 dB. This Channel-II brieftone is clearly visible on Channel-I spectra (Figure 4(a)), although greatly attenuated. This is a clear indication of the effect of Channel-I AGC (due to a Channel-I heterodyne) on the cross-talk level. This also indicates that the Channel-II cross-talk was already present in Channel-I signal when it was being received by the Channel-I radio receiver/recorder. In the other two phrases also we find similar indications of cross-talk being received over the radio. This rules out the possibility of it being superimposed later acoustically or electrically.
Next, we examine the "Stemmons" phrase (Figure 8). In this segment, a Channel-I heterodyne ends (at 21.23 seconds, Channel-I time) just before the Channel-II communication begins (at 14.18 seconds, Channel-II time). During the first Channel-II brief tone (14.25 to 14.51 seconds, Channel-II time), T(t) function is increasing rapidly, registering a gain of about 10 dB. This indicates recovery of Channel-I AGC at the end of the heterodyne. There is a brief Channel-I heterodyne from 22.41 to 22.49 seconds, Channel-I time). This heterodyne is different from others in that it is around 1200 Hz while others are around 2500 Hz. Nevertheless, this heterodyne also activates the Channel-I AGC which is evident from the total Channel-I energy plot as well as the T(t) plot. Following this heterodyne the recovery is slow, taking about a second or so. There is another Channel-I heterodyne from 25.81 to 26.30 seconds, Channel-I time. A Channel-II brieftone was already present when this heterodyne began. The dramatic effect of Channel-I AGC, due to the heterodyne, is evident in T(t) plot which drops by more than 15 dB over a very short period. This is also clear on Figure 5(a) where the intensity of the Channel-II brief tone dramatically reduces as soon as the Channel-I heterodyne begins.
Finally, we examine the crucial "Hold-Everything" phrase (Figure 6) in the light of the above discussion. On Figure 6, we have also marked the timings of the third and fourth "shots" identified by BRSW and WA. The third "shot" is supposed to be a "shot" from the grassy knoll area. As mentioned before, this segment of Channel-I is very noisy. During this period, total Channel-I energy is also fluctuating widely. Due to the noisy conditions, the T(t) function is less stable, but, still we can see the effect (on T(t)) of the Channel-I AGC due to the two heterodynes present during this segment. This is particularly pronounced during the second heterodyne. This part is expanded and shown in more detail in Figure 9. A Channel-II brief tone had begun just before this heterodyne. Due to the Channel-I AGC action, the T(t) function drops by about 14 dB and then it appears to increase. This increase in T(t) estimate is perhaps due to presence of Channel-I noise in brief tone frequency bins. As explained before, the T(t) estimate is an upper bound, and the actual T(t) is likely to be smaller. The Channel-II brief tone reappears shortly after the heterodyne ends. During this AGC recovery phase, T(t) is steadily increasing, starting from a very low value and almost reaching the pre-heterodyne level. In this part also, some T(t) values are considerably higher than indicated by the general trend, due again to Channel-I noise present during this period. On Figure 3(a), we can clearly see (11.02 to 11.18 seconds, Channel-I time) a gradual buildup of the Channel-II brieftone as reflected on Channel-I.
From the above discussion, we come to a firm conclusion that Channel-II cross-talk was already present in the Channel-I radio signal when it was being received over the radio. This rules out the possibility of it being acoustically or electrically superimposed later. This is also true for the crucial "Hold-Everything" phrase which is supposed to contain the so-called "shots."
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