High Dynamic Range Resampling for Software Radio

Authors: Arthur David Snider, Laiq Azam

Abstract:

The classic problem of recovering arbitrary values of a band-limited signal from its samples has an added complication in software radio applications; namely, the resampling calculations inevitably fold aliases of the analog signal back into the original bandwidth. The phenomenon is quantified by the spur-free dynamic range. We demonstrate how a novel application of the Remez (Parks- McClellan) algorithm permits optimal signal recovery and SFDR, far surpassing state-of-the-art resamplers.

Keywords: Sampling methods, Signal sampling, Digital radio, Digital-analog conversion.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332414

References:

[1] J. R. Higgins, "Five Short Stories About the Cardinal Series," Bull. Amer. Math. Soc., vol. 12, no. 1, pp. 45-89, 1985.
[2] P. L. Butzer, W. Splettstosser and R. L. Stens, "The Sampling Theorem and Linear Prediction in Signal Analysis," Jber. d. Dt. Math.- Verein. vol. 90, pp. 1-70, 1988.
[3] P. L. Butzer and R. L. Stens, "Sampling Theory for Not Necessarily Band-Limited Functions: A Historical Review" SIAM Rev., vol. 34, no. 1, pp. 40-53, 1992.
[4] A. G. Garcia, "Orthogonal Sampling Formulas: A Unified Approach," SIAM Rev., vol. 42, no. 3, pp. 499-512, 2000.
[5] A. J. Jerri, "The Shannon Sampling theorem - Its Various Extensions and Applications: a Tutorial Review," Proc. IEEE, vol. 65, no. 11, pp. 1565- 1596, 1977.
[6] M. Unser, "Sampling - 50 Years After Shannon," Proc. IEEE, vol. 88, no. 4, pp. 569-587, April 2000.
[7] A. I. Zayed, Advances in Shannon-s Sampling Theorem, Boca Raton, FL: CRC Press, 1993.
[8] C. W. Farrow, "A Continuously Variable Delay Element," ISCAS -88, IEEE 1988.
[9] H. D. Helms and J. B. Thomas, "Truncation Error of Sampling-Theorem Expansions," Proc. IRE, vol. 50, pp. 179-184, Feb. 1962.
[10] D. Jagerman, "Bounds for Truncation Error of the Sampling Expansion," SIAM J. App. Math., vol. 14, no. 4, pp. 714- 723, July 1966.
[11] L. J. Karam and J. H. McClellan, "Complex Chebychev Approximation for FIR Filter Design," IEEE Trans. Circ. & Syst., vol. 42, no. 3, pp. 207- 215, March 1995.