The pulse of incremental encoder！

Consider the two quadrature pulse signals (say, A and
B) from an incremental encoder. Using sketches of
these signals, show that in one direction of rotation,
signal B is at a high level during the up-transition of
signal A, and in the opposite direction of rotation,
signal B is at a low level during the up-transition of
signal A. Note that the direction of motion can be
determined in this manner by using level detection of
one signal during the up-transition of the other signal.

A shaft encoder that has N windows per track is
connected to a shaft through a gear system with gear
ratio p. Derive formulas for calculating angular
velocity of the shaft by (a) the pulse-counting method,
and (b) the pulse-timing method. What is the speed
resolution in each case? What effect does the step-up
gearing have on the speed resolution?

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