Real-time estimation and prediction of periodic signals from attenuated and phase-shifted sensed signals

The use of linear filters to extract desired signals from sensed signals which contain a mixture of the desired and undesired signals inherently alters amplitude and phase characteristics of the desired signals. Attenuation and phase-shift incurred in the extracted desired signals is undesirable in applications such as real-time physiological tremor compensation. Algorithms based on Fourier linear combiners (FLC) such as a weighted-frequency Fourier linear combiner (WFLC), and a bandlimited multiple Fourier linear combiner (BMFLC) can estimate and extract periodic signals without altering the amplitude and phase characteristics. The proper performance of the algorithms usually requires prefiltering of the sensed signals using linear filters. Moreover, in some situations, the sensed signals have been prefiltered by inevitable linear filters present in the sensors or sensor modules. Modification made to WFLC and BMFLC to compensate for the change in amplitude and phase characteristics of the extracted desired periodic signals due to the prefiltering for real-time applications is presented. A way to perform prediction of a periodic signal using the WFLC or BMFLC algorithm is also shown.