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The realisation of finite-sample frequency-selective filters

By D.S.G. Pollock


This paper shows how a frequency-selective filter that is applicable to short trended data\ud sequences can be implemented via a frequency-domain approach. A filtered sequence\ud can be obtained by multiplying the Fourier ordinates of the data by the ordinates of the\ud frequency response of the filter and by applying the inverse Fourier transform to carry\ud the product back into the time domain. Using this technique, it is possible, within\ud the constraints of a finite sample, to design an ideal frequency-selective filter that will\ud preserve all elements within a specified range of frequencies and that will remove all\ud elements outside it.\ud Approximations to ideal filters that are implemented in the time domain are\ud commonly based on truncated versions of the infinite sequences of coefficients derived\ud from the Fourier transforms of rectangular frequency response functions. An alternative\ud to truncating an infinite sequence of coefficients is to wrap it around a circle of a\ud circumference equal in length to the data sequence and to add the overlying coefficients.\ud The coefficients of the wrapped filter can also be obtained by applying a discrete Fourier\ud transform to a set of ordinates sampled from the frequency response function. Applying\ud the coefficients to the data via circular convolution produces results that are identical\ud to those obtained by a multiplication in the frequency domain, which constitutes a\ud more efficient approach

Topics: Linear filtering, Frequency-domain analysis
Publisher: Dept. of Economics, University of Leicester
Year: 2008
OAI identifier:

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