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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:53629", author = "Arthur David Snider and Laiq Azam", title = "High Dynamic Range Resampling for Software Radio", 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.", volume = "1", number = "6", pages = "824-6", }