Information gain for the pulse width modulation of a square waveform by continued signal tracking through a second pulse

摘要

We continue the analysis of information about the pulse width modulation of a square wave signal to derive the posterior density of the pwm ratio given digital counts of on and off components of two pulses when the second is an exact replica of the first. A propagation equation for the phase shift disturbance allows that sequential counts, which can occur in only seven distinct structures, rule out various portions of the unit cube as containing the unknown disturbance fractions. Again, the analysis uses only elementary arguments in the calculus of many variables, but the structure of the setup becomes extremely complicated. We provide complete analysis in the simplest of the seven cases, and display the resulting posterior distribution and density properties under the condition of the two-pulse counts being M₁= 100, N₁= 1000, M₂= 101, and N₂= 1001. Algebraic and graphical detail is produced using MAPLE software.