least squares acceleration filtering for the estimation of signal derivatives and sharpness at extrema a family of finite impulseresponse fir filters is derived which estimate the second derivative or acceleration of a digitized signal the acceleration is obtained from parabolas that are continuously fit to the signal using a least squares optimization criterion a closedform solution for the filter coefficients is obtained the general approach is computationally simple can be performed in realtime and is robust in the presence of noise an important application of the method that of measuring sharpness in biologic signals is presented using the electroencephalogram eeg and electrocardiogram ekg signals as examples furthermore the design method is extended to derive fir filters for estimating derivatives of arbitrary order in digital signals of biologic or other origins