US Patent 7587442 Method of determining the derivative of an input signal

The derivative of a noise-containing input signal is determined by using an aliased derivative to periodically reset a filtered version of a normally determined derivative. The aliased derivative is calculated using a slower update or sampling rate than the normally determined derivative, and the filtered version of the normally determined derivative is reset to a reset value at each update of the aliased derivative. The reset value is based on a weighted sum of the aliased derivative and the filter output. The periodically reset filter output closely follows an idealized derivative of the input signal, substantially eliminating the phase delay introduced by conventional filtering.