Improving accuracy of FIR filters for computing convolution transforms for smooth non-bandlimited signals

Abstract

We propose to improve the accuracy of FIR filters for computing convolution transforms for smooth non-bandlimited (NBL) signals by designing filters by the identification method with using a pair of bandlimited portions of the chosen NBL input and output signals related with each other by the given transform. A design example of type IV linear phase differentiator is presented, where filter coefficients are calculated from the bandlimited portions of the Cauchy pulse and its derivative. The performance of the designed differentiator is evaluated by comparing the accuracy of computed derivatives for several smooth NBL test signals, such as the Cauchy pulse, the Hilbert transform of Cauchy pulse, the Gaussian function, as well as for a bandlimited sinc-function. Evaluation results demonstrate that the proposed design method generates more accurate differentiators than the Parks-McClellan algorithm, the impulse response truncation method and the identification with using full-band Cauchy pulse and its derivative.