Independently toggling two series switches to multiply two pwm signals
I know nothing about MathLab and a little about PWM. ;^)


  It is known that one can synthesize a signal into a train of boxcar pulses, each with the same amplitude, if proper low pass filtration is applied to this pulse train before it reaches the load a.k.a pwm modulation. 


If you low-pass filter it it's no longer PWM - it's an analog signal.


  Now consider the synthesis of the product of two signals. I have found with some rudimentary matlab simulation (see below) that the average* of the multiplication of two pwm modulated constant** values is equal to the value of the multiplication of two constant signals 


You've got to be careful here.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Multiplying these two PWM signals (in an AND fashion) gives zero output.







simulate this circuit

Figure 2. If one frequency is a high multiple of the other the scheme could work.







simulate this circuit

Figure 3. A mixed analog-digital multiplier might also satisfy your requirements. A is an analog signal (which may have been generated by a PWM source). B could be digital or analog.

There was a digital piano chip available in the 1980s (used by Maplin and Elektor in their digital pianos) that generated an RC decay curve every time a note was triggered. This was toggled by the digital tone generator pulse trains to give a pulse train of decaying square-waves. (These were then filtered to take out the very high harmonics.) The square waves gave only odd harmonics. I livened mine up by adding in the octave above each note using 60 diode OR gates - one for each key. It helped.