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Statistical Approach to Basis Function Truncation in Digital Interpolation Filters

Authors: F. Castillo, J. Arellano, S. Sánchez


In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.

Keywords: Interpolation, basis function, over-sampling

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[1] Farokh Marvasti (ed.), Nonuniform Sampling, Theory and Practice (Kluwer Academic/Plenum Publishing, 2001).
[2] S. Mitra, Digital Signal Processing: A Computer-Based Approach, 3rd edition. (McGraw-Hill International Press, 2005).
[3] Steven W. Smith, The Scientist and Engineer-s Guide to Digital Signal Processing, 2nd edition (California Technical Publishing, 1999).
[4] Analog Devices Engineering Staff, Mixed-Signal and DSP Design Techniques, ed. Walt Kester (USA, 2000).
[5] Thomas Strohmer, Implementations of Shannon's Sampling Theorem: A Time-Frequency Approach. Sampling Theory in Signal and Image Processing (Sampling Publishing, Jan. 2005).
[6] R. L. Stratonivich, Topics in the Theory of Random Noise (Gordon and Breach, 1963).
[7] V. A. Kazakov, Sampling-Reconstruction Procedure of Gaussian Fields. Abstracts of the International Conference ''Sampling Theory and Applications'' (SAMPTA 2003), (Strobl, Salzburg, Austria, May 2003).
[8] Vladimir Kazakov and Sviatoslav Afrikanov, Sampling - Reconstruction Procedure of Gaussian Fields, Computaci├│n y Sistemas, CIC-IPN, 9/3 (2006).
[9] Daniel Salda├▒a Rodr├¡guez, Estudio del procedimiento de muestreoreconstrucci├│n de los procesos Gaussianos con una cantidad de muestras limitada (Master-s thesis, ESIME-IPN, México DF, 2003).
[10] I. Mednieks, Methods For Spectral Analysis Of Nonuniformly Sampled Signals. (International Conference on Sampling Theory and Application, SAMPTA 2005).
[11] Jes├║s Bernal Berm├║dez and Jes├║s Bobadilla, Reconocimiento de voz y fonética ac├║stica (Alfaomega, Espa├▒a, 2003).
[12] Saeed Mian Qaisar and Laurent Fesquet. Adaptive Rate Sampling and Filtering for Low Power Embedded Systems (International Conference on Sampling Theory and Application, SAMPTA 2007).
[13] National Semiconductor, ADC16071/ADC16471, 16-Bit Delta-Sigma 192 ks/s Analog-to-Digital Converters (Datasheet, 1995).
[14] A. V. Oppenheim and R. W. Schafer, with J. R. Buck, Discrete-Time Signal Processing, 2nd edition (Prentice-Hall, Inc., Upper Saddle River, NJ, 1999).
[15] Cormac Herley and Ping Wah Wong, Minimum Rate Sampling and Reconstruction of Signals with Arbitrary Frequency Support. (IEEE Transactions on Information Theory, July 1999).