### Estimation of Length and Order of Polynomial-based Filter Implemented in the Form of Farrow Structure

#### Abstract

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.

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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

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

T. Saramaki, “Finite impulse response filter design”, in Handbook for Digital Signal Processing, John Wiley & Sons, New York, USA, 1993

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