The eZee detection is the common one of a ring of magnets in a disc behind the chainwheel which are sensed by a semiconductor Hall effect sensor as they pass. In pedelec mode, there's no drive if they aren't sensed passing by continuously. The magnet spacing and hence sensing frequency can be a way of fixing a relative speed for various degrees of power, for example in giving a power phase down from about 13 mph in accordance with European law.
The Giant system using the Panasonic motor unit is much more complex. It has an internal pedal sensing drum assembly to sense rotation, speed and relative pedal effort, and a sensor which reads off the motor output gear train which determines the motor output speed and power contribution relative to the pedal input. The multiple signals from these are computed on the mainboard and summed in various proportions to determine the assistance level to be applied in any particular circumstance.
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