{"title":"Statistical Approach to Basis Function Truncation in Digital Interpolation Filters","authors":"F. Castillo, J. Arellano, S. S\u00e1nchez","volume":39,"journal":"International Journal of Electronics and Communication Engineering","pagesStart":480,"pagesEnd":485,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/13816","abstract":"In this paper an alternative analysis in the time\r\ndomain is described and the results of the interpolation process are\r\npresented by means of functions that are based on the rule of\r\nconditional mathematical expectation and the covariance function. A\r\ncomparison between the interpolation error caused by low order\r\nfilters and the classic sinc(t) truncated function is also presented.\r\nWhen fewer samples are used, low-order filters have less error. If the\r\nnumber of samples increases, the sinc(t) type functions are a better\r\nalternative. Generally speaking there is an optimal filter for each\r\ninput signal which depends on the filter length and covariance\r\nfunction of the signal. A novel scheme of work for adaptive\r\ninterpolation filters is also presented.","references":"[1] Farokh Marvasti (ed.), Nonuniform Sampling, Theory and Practice\r\n(Kluwer Academic\/Plenum Publishing, 2001).\r\n[2] S. Mitra, Digital Signal Processing: A Computer-Based Approach,\r\n3rd edition. (McGraw-Hill International Press, 2005).\r\n[3] Steven W. Smith, The Scientist and Engineer-s Guide to Digital\r\nSignal Processing, 2nd edition (California Technical Publishing,\r\n1999).\r\n[4] Analog Devices Engineering Staff, Mixed-Signal and DSP Design\r\nTechniques, ed. Walt Kester (USA, 2000).\r\n[5] Thomas Strohmer, Implementations of Shannon's Sampling Theorem:\r\nA Time-Frequency Approach. Sampling Theory in Signal and Image\r\nProcessing (Sampling Publishing, Jan. 2005).\r\n[6] R. L. Stratonivich, Topics in the Theory of Random Noise (Gordon\r\nand Breach, 1963).\r\n[7] V. A. Kazakov, Sampling-Reconstruction Procedure of Gaussian\r\nFields. Abstracts of the International Conference ''Sampling Theory\r\nand Applications'' (SAMPTA 2003), (Strobl, Salzburg, Austria, May\r\n2003).\r\n[8] Vladimir Kazakov and Sviatoslav Afrikanov, Sampling -\r\nReconstruction Procedure of Gaussian Fields, Computaci\u251c\u2502n y\r\nSistemas, CIC-IPN, 9\/3 (2006).\r\n[9] Daniel Salda\u251c\u2592a Rodr\u251c\u00a1guez, Estudio del procedimiento de muestreoreconstrucci\u251c\u2502n\r\nde los procesos Gaussianos con una cantidad de\r\nmuestras limitada (Master-s thesis, ESIME-IPN, M\u00e9xico DF, 2003).\r\n[10] I. Mednieks, Methods For Spectral Analysis Of Nonuniformly\r\nSampled Signals. (International Conference on Sampling Theory and\r\nApplication, SAMPTA 2005).\r\n[11] Jes\u251c\u2551s Bernal Berm\u251c\u2551dez and Jes\u251c\u2551s Bobadilla, Reconocimiento de voz\r\ny fon\u00e9tica ac\u251c\u2551stica (Alfaomega, Espa\u251c\u2592a, 2003).\r\n[12] Saeed Mian Qaisar and Laurent Fesquet. Adaptive Rate Sampling and\r\nFiltering for Low Power Embedded Systems (International\r\nConference on Sampling Theory and Application, SAMPTA 2007).\r\n[13] National Semiconductor, ADC16071\/ADC16471, 16-Bit Delta-Sigma\r\n192 ks\/s Analog-to-Digital Converters (Datasheet, 1995).\r\n[14] A. V. Oppenheim and R. W. Schafer, with J. R. Buck, Discrete-Time\r\nSignal Processing, 2nd edition (Prentice-Hall, Inc., Upper Saddle\r\nRiver, NJ, 1999).\r\n[15] Cormac Herley and Ping Wah Wong, Minimum Rate Sampling and\r\nReconstruction of Signals with Arbitrary Frequency Support. (IEEE\r\nTransactions on Information Theory, July 1999).","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 39, 2010"}