Models of bias of mean square value digital estimator for selected deterministic and random signals

• Autorzy: Lal-Jadziak J. , Sienkowski S.
• Języki publikacji: EN

Abstrakty

EN

The article presents the probability density functions as well as characteristic functions of selected periodic and random signals. On their basis, original models of the bias of the mean square value digital estimator have been designed. These models were employed in investigating estimation errors caused by analog to digital conversion and analog to digital conversion with a dither signal. Selected graphical model representations and their analyses are demonstrated. It has been shown that for a triangular probability density function random signal with the amplitude At = kq, k∈N \ {0}, mean square value reconstruction occurs on the basis of a signal quantized with the accuracy of Sheppard's correction. Whereas for periodic signals as well as for the sum of periodic and random signals, the δ component of bias due to the nonsatisfaction of the reconstruction condition is a suppressed oscillating function of the quotient of the amplitude A and the quantization step size q. It has been proved that by adding, prior to quantization, a triangular distribution random signal with zero mean and the amplitude At = kq (k = 1, 2, ...) in the mean square value measurement of any periodic signal, this bias component can be brought to zero.

Słowa kluczowe

EN

probability density function; characteristic function; Widrow's theory of quantization; mean square value; estimator bias

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2008
• Tom: Vol. 15, nr 1
• Strony: 55--67
• Opis fizyczny: Bibliogr. 13 poz., rys., tab., wykr.

Twórcy

autor

Lal-Jadziak J.

autor

Sienkowski S.

• Nicolaus Copernicus University, Institute of Physics, Toruń, Poland,

Bibliografia

• 1. Domańska A.: “Influencing the reliability in measurement systems by the application of A-D conversion with dither signal”, Rozprawy, no. 308, Poznań, Wyd. Pol. Poznańskiej 1995. (in Polish)
• 2. Lal-Jadziak J.: “Influencing Accuracy in Correlation Measurements”, Monografia, no. 101, Wyd. Pol. Zielonogórskiej, Zielona Góra 2001. (in Polish)
• 3. Lal-Jadziak J.: “The influence of quantizing on the accuracy of mean square value estimation”, Pomiary Automatyka Kontrola, no. 7/8, 2002, pp. 61-64. (in Polish)
• 4. Kollar I.: “Bias of mean value and mean square value measurements based on quantized data”, IEEE Trans. Instrum. Meas., vol.43, no. 5, 1994, pp.733-739.
• 5. Pacut A.: Probability. Theory. Probabilistic modelling in technology. Warszawa, WNT 1985. (in Polish)
• 6. Mariano J. L., Ramos H.: “Validity of Widrow’s model for sinusoidal signals”, Measurement, vol. 39, no. 3, 2006, pp. 198-203.
• 7. Sienkowski S.: “Modeling characteristic functions of determined and random signals in LabWINDOWS”, 1st International Conference For Young Researchers, Zielona Góra, 2006.
• 8. Hasse L., Spiralski L.: Noise of electronic elements and circuits. Warszawa, WNT 1981. (in Polish)
• 9. Lal-Jadziak J., Sienkowski S.: “Modeling of bias of mean square value estimator for selected signals”, Pomiary Automatyka Kontrola, no. 9 BIS, 2007, pp. 93-97. (in Polish)
• 10. Widrow B., Kollar I., Liu M.-C.: “Statistical theory of quantization”, IEEE Trans. Instrum. Meas., vol. 45, no. 2, 1996, pp. 353-361.
• 11. Widrow B., Kollar I.: Quantization Noise - A Book on Uniform and Floating-Point Quantization, Budapest 2006. http://www.mit.bme.hu/books/quantization/
• 12. Sripad B., Snyder D.: “A necessary and sufficient condition for quantization errors to be uniform and white”, IEEE Trans. Acoust. Speech, Signal Process., vol. ASSP-25, no. 5, 1977, pp. 442-448.
• 13. Wagdy M.F.: “Effect of various dither forms on quantization errors of ideal A/D converters”, IEEE Trans. Instrum. Meas., vol. 38, 1989, pp. 850-855.