Estimation of Length and Order of Polynomial-based Filter Implemented in the Form of Farrow Structure
Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP) to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.
Keywords:digital filters, filter design, polynomial-based filters, Farrow structure
J. Vesma, T. Saramaki, “Polynomial-based interpolation Filters-Part I: Filter synthesis”, Circuits, Systems, and Signal Processing, Vol. 26, No 2, pp. 115-146, 2007 DOI: https://doi.org/10.1007/s00034-005-0704-8
C. W. Farrow, “A continuously variable digital delay element”, IEEE International Symposium on Circuits and Systems, pp. 2641-2645, Espoo, Finland, June 7-9, 1988
D. Babic, T. Saramaki, M. Renfors, “Conversion between arbitrary sampling rates using polynomial-based interpolation filters”, 2nd International TICSP Workshop on Spectral Methods and Multirate Signal Processing, pp. 57-64, Toulouse, France, 2002
J. F. Kaiser, “Nonrecursive digital filter design using the I0-sinh window function”, IEEE International Symposium on Circuits and Systems, pp. 20-23, 1974
T. Saramaki, Multirate signal processing, Lecture Notes, Tampere University of Technology, Finalnd, 2012 available at: http://www.cs.tut.fi/~ts/
D. Babic, H. G. Gockler, “Estimation of the length and the polynomial order of polynomial-based filters”, 8th International Conference on Sampling Theory and Applications, Marseille, France, May 18-22, 2009
D. Babic, “Estimation of the number of polynomial segments and the polynomial order of prolonged Farrow structure”, 22nd Telecommunications Forum Telfor (TELFOR), Belgrade, Serbia, pp. 461 - 464, November 25-27, 2014 DOI: https://doi.org/10.1109/TELFOR.2014.7034446
T. Saramaki, “Finite impulse response filter design”, in Handbook for Digital Signal Processing, John Wiley & Sons, New York, USA, 1993
How to Cite
MetricsAbstract Views: 447
PDF Downloads: 235
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.