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Realisations of Finite-Sample Frequency-Selective Filters

By D.S.G. Pollock

Abstract

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

Topics: Signal extraction, Linear filtering, Frequency-domain analysis
Publisher: Dept. of Economics, University of Leicester
Year: 2008
OAI identifier: oai:lra.le.ac.uk:2381/7563

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Citations

  1. (2005). A frequency selective filter for short-length time series. doi
  2. (1999). A Handbook of Time-Series Analysis, Signal Processing and Dynamics. doi
  3. (2002). Circulant matrices and time-series analysis. doi
  4. (2004). Computation of asymmetric signal extraction filters and mean squared error for ARIMA components models. doi
  5. (2002). Demetra 2.0 User Manual: Seasonal Adjustment Interface for Tramo/Seats and X12-ARIMA. the Statistical Office of the European Communities.
  6. (1997). Fitting time series models by minimising multistep-ahead errors: a frequency domain approach. doi
  7. (2005). Forecasting and signal extraction with misspecified Models. doi
  8. (1976). Fourier Analysis of Time Series: An Introduction. doi
  9. (2003). Frequency Domain Analyses of SEATS and X–11/12–ARIMA Seasonal Adjustment Filters for Short and Moderate-Length Time Series.
  10. (1999). Measuring business cycles: approximate bandpass filters for economic time series. doi
  11. (1946). Measuring Business Cycles. doi
  12. (1998). New capabilities and methods of the X12-ARIMA seasonal adjustment program. doi
  13. (1916). Note on graduation by adjusted averages.
  14. (2004). Program TSW: Revised Reference Manua. Working Paper, Research Department, Banco de Espan˜a.
  15. (2003). The bandpass filter. doi

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