Narrow-Band Low-Pass Differentiators

Narrowband lowpass digital differentiator design (pdf file, 200 KB)
I. W. Selesnick. In Conf. Rec. Thirty-Sixth Asilomar Conf. on Signals, Systems and Computers, vol. 1, pages 360-364, CA, November 3-6, 2002.

slides (pdf file, 236 KB)

MATLAB programs: lpdiff.m, test1.m

Abstract: This paper describes a simple formulation for the non-iterative design of narrowband FIR linear-phase lowpass digital differentiators. The filters are flat around dc and have equally spaced nulls in the stopband. The impulse response can be written as a sum of cosines. The design problem is formulated so as to avoid the complexity or ill-conditioning of the standard method for the design of similar filters when those methods are used to design narrow band filters with long impulse responses. Narrowband lowpass differentiators have applications in the detection of transient events in noisy signals. An example of saccade detection in EOG signals is provided to illustrate the lowpass requirement of the filter.