An Approach to Accurate Inversion of Convolution Transforms by FIR Filters

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Abstract: Inversion of convolution transforms is considered by FIR filters for aperiodic band- and time-unlimited signals from the perspective attaining maximum accurate inverted waveforms with controllable noise amplification of the filter. The difficulties hampering to gain this goal, such as a lack of knowledge how the digital filter shall deviate from ideal one to produce waveforms as accurately as possible, complexity to choose optimal sampling rate, necessity to sacrifice the accuracy for suppressing noise, etc. are analysed. Based on learning in the input-output signal domain and controlling noise amplification by varying sampling rate, an approach is developed for designing maximum accurate filters, which are specified only by two user’s relevant parameters: (i) the desired noise gain and (ii) the continuous time support. Implementation of the approach is illustrated by designing a digital differentiator for the logarithmic derivative and a digital estimator of the distribution of relaxation times. Simulation results are presented demonstrating that the approach allows constructing more accurate FIR filters with predefined noise amplification and support sizes compared with those designed by other commonly used techniques.

WSEAS Transactions on Signal Processing, ISSN / E-ISSN: 1790-5052 / 2224-3488, Volume 10, 2014, Art. #25

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Vairis Shtrauss, "An Approach to Accurate Inversion of Convolution Transforms by FIR Filters," WSEAS Transactions on Signal Processing, vol. 10, pp. 242-253, 2014, DOI:
Vairis Shtrauss. An Approach to Accurate Inversion of Convolution Transforms by FIR Filters. WSEAS Transactions on Signal Processing. 2014;10:242-253.
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