David Reaves said:
It's my understanding that, using the current DSB stereo FM standards, L-R energy gets to 'sneak in' under L+R's level (especially important when composite clipping is applied), because its peak level is generally 6 dB lower than that of the Main Channel L+R's.
If I am following the SSB thread correctly, it would appear that by bumping up its peak level by 6 dB, the L-R must then accept an equivalent amount of increased clipping (or other processing) with regard to that which may be generally applied present-day to a composite signal.
At the moment, I don't have the means to test this, but I would surmise that 6dB more L-R clipping than present practices may have a serious downside. Or am I off-base? Composite processing is already really pushing the quality-perception envelope. At the least, I would anticipate SSB will thus have a different sound texture than the DSB stereo we all grew up with.
My white paper discusses the peak modulation of SSB in considerable detail. Assuming that the SSB modulator introduces no group delay distortion, and assuming that the audio processing applied to the DSB and SSB generators is the same, the following conditions will produce the same modulation in the DSB and SSB cases:
1. Pure L+R
2. Pure L-R
3. Single-channel only
4. in-phase material panned anywhere in the stereo soundfield (i.e. what would occur if you took a mono track and panned it from fully left to fully right)
What *does* cause overshoots in the SSB modulation is material that is uncorrelated on the left and right channels. The "two identical sinewaves with 90 degrees phase shift between them" that I discussed in my white paper may be the worst case, producing about 138% modulation (assuming 9% pilot injection).
The best way to get a gut feel for this is to look at the composite waveforms on an oscilloscope and realize that the SSB subchannel does not interleave with the main channel; it adds to it. The SSB modulator takes the L-R, inverts the spectrum, and arithmetically frequency-shifts it upward by 38 kHz. A simple example is 1 kHz left-only modulation, which will produce equal amplitude 1 kHz and 37 kHz sinewaves in the composite. At certain times, the peaks of the 1 kHz and 37 kHz sinewaves will coincide, producing peak modulation that is twice that of the 1 kHz and 37 kHz tones considered separately.
Because of the loss of phase coherence between the L+R and L-R signals caused by the frequency shift and spectral inversion (even in an SSB modulator that adds no excessive group delay distortion because its lowpass filters or Hilbert transformers have linear phase), the worst-case peak modulation is the sum of the magnitudes of the L+R and L-R signals. There is no interleaving, unlike the DSB system. If you look at Fig. 11 in my paper (the vector summation of left and right signals to produce the L+R and L-R signals), it is clear that in the worst case, the sum of the magnitudes of the L+R and L-R signals can cause the peak modulation to increase by a factor of SQRT(2) (141%) compared to the peak modulation produced by the DSB system. When you add the pilot tone into the picture, the worst-case overshoot becomes about 138% because the pilot modulation is the same for both systems.
While I can't yet prove mathematically that the maximum overshoot for arbitrary signals in the left and right channels is also 138%, my intuition suggests that it is. I base my argument on the fact that peak modulation is an instantaneous measurement, so the modulation measurement criterion is simple compared to, for example, r.m.s., which involves an integration over time. If you look at Fig 11 in terms of the vector sum and difference of L and R, there is no combination of L and R that can cause the instantaneous sum of |L+R| + |L-R| to be more than 2 * SQRT(2), assuming that |L| and |R| are both constrained to 1 by the audio processor preceding the stereo encoder and that the SSB generator's filters have constant group delay so they do not cause this constraint to be violated. (The |x| notation means that you take the magnitude, i.e. the length of the vector, ignoring the phase.)
The 90 degree relationship is also known mathematically as a "quadrature" relationship and is related to the mathematical concept of "linear independence." My working hypothesis is that linearly independent left and right signals whose magnitudes are constrained to 1 and whose bandwidths are constrained to less than 19 kHz can produce overshoots as large as 138 % modulation but no larger in the SSB system. This hypothesis could be falsified by anyone who could supply an example of a pair of L and R signals that met this criterion but produced larger overshoots. While I don't want to take the time to do this right now, it would be worthwhile to consider combinations of sinewaves making up the Fourier elements of a squarewave because once can choose combinations whose peak level is lower than the peak level of the sum of the magnitudes of individual sinewaves.
Exercise for the reader: consider the sum of a 1 kHz and 3 kHz sinewave, where the amplitude of the 3 kHz sinewave is 11.11...% of the amplitude of the 1 kHz sinewave and they are phase-locked such that every zero crossing of the 1 kHz sinewave is time-coincident with the zero-crossing of the 3 kHz sinewave.
or expressed as an equation
L = 1.125 [SIN(2 pi 1000 t) + 0.1111 SIN(2 pi 3000 t)]
(The 1.125 factor makes the maximum peak level of L = 1.)
Find an R signal that meets the "magnitude<= 1" and bandwidth constraints that causes the SSB peak modulation to exceed 138%.
Bob Orban
