The Realisation of Finite-Sample Frequency-Selective Filters
This paper shows how a frequency-selective filter that is applicable to short trended data sequences can be implemented via a frequency-domain approach. A filtered 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 into 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.
|Date of creation:||Apr 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +44 (0)116 252 2887
Fax: +44 (0)116 252 2908
Web page: http://www2.le.ac.uk/departments/economics
More information through EDIRC
|Order Information:|| Web: http://www2.le.ac.uk/departments/economics/research/discussion-papers Email: |
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Alain Noullez & Alessandra Iacobucci, 2004.
"A Frequency-selective Filter for Short-Length Time Series,"
Computing in Economics and Finance 2004
128, Society for Computational Economics.
- Alessandra Iacobucci & Alain Noullez, 2005. "A Frequency Selective Filter for Short-Length Time Series," Computational Economics, Society for Computational Economics, vol. 25(1), pages 75-102, February.
- Alessandra Iacobucci & Alain Noullez, 2004. "A Frequency Selective Filter for Short-Length Time Series," Documents de Travail de l'OFCE 2004-05, Observatoire Francais des Conjonctures Economiques (OFCE).
When requesting a correction, please mention this item's handle: RePEc:lec:leecon:08/13. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mrs. Alexandra Mazzuoccolo)
If references are entirely missing, you can add them using this form.