Deconvolution filtering plays an important role in such situations where one wants to invert an effect of the linear filtering process described by the operation of convolution. As a rule, deconvolution represents a class of ill-posed problems for which solutions are usually unstable or numerically ill-conditioned. In this contribution an application of a FIR, (Finite Impulse Response), deconvolution filter with respect to the odd pair of impulses, for processing market data, is discussed. The optimum Chebyshev minimax norm solution for this case of deconvolution filtering has been first presented in [1]. In principle the said deconvolution filter should be considered as a specific integrator i.e., averaging filter. The mean value of impulse response of a typical averaging filter is a positive number, which results in averaging the mean value of input signal. However, the mean value of the Chebyshev deconvolution filter here discussed equals zero, which results in integrating the varying part of the input signal only. Using numerical computations, it was found that the first order difference (numerical derivative) of the output of the Chebyshev deconvolution filter is strongly correlated, (> 95%), with the de-trended value of the input signal. Computations were carried out using one-minute quotations for the futures contracts on WIG 20, Warsaw Stock Exchange index, covering period of time from October 30,2001 thru June 16, 2003, (ca. 145000 samples). This shows that output of the Chebyshev deconvolution filter here presented is a good estimate of the de-trended data averaged in a finite length window.

[1] Andrzej DYKA, Chebyshev minimax deconvolution filtering for a pair of discrete pulses, International Journal for Computation and Mathematics in Electrical and Electronic Engineering - COMPEL, vol. 9 No. 2, 1990, pp. 59-65. Can be downloaded from www.dyka.info.pl

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