Rotational Rate Gradient Determination Using Variable Window Filtering

The patent changes the parameter of gradient calculation by using a time-dependent gradient function that adapts to the current rotational state. Instead of fixed high-frequency sampling, the system calculates gradients based on variable time intervals between tooth passages, with the gradient formula incorporating the actual measured times ti. This parameter adaptation reduces noise while maintaining precision across different rotational speeds.

The patent applies preliminary action by pre-calculating and storing time stamps for each tooth passage event. These time stamps are recorded as the element rotates, and the gradient is subsequently calculated using these pre-captured time values. This approach allows gradient determination without real-time filtering that would cause phase shift, as all necessary data is captured at the moment of tooth passage.

The patent implements dynamics by making the sampling interval adaptive rather than fixed. The system determines rotational rate using the actual time intervals between consecutive tooth passages, which dynamically adjust based on the current rotational speed. When rotation is slow, larger time intervals are naturally accommodated; when rotation is fast, smaller intervals are captured. This dynamic approach ensures continuous rotational rate information is available across all speed ranges.

The patent introduces an intermediary element in the form of a time-dependent gradient calculation function that mediates between the raw tooth passage times and the final rotational rate gradient. Instead of directly applying simple difference quotients to noisy signals, the system uses the intermediate time stamps ti of actual tooth passages to calculate gradients through a formulated approach that inherently filters noise while maintaining computational simplicity.