Quantization error analysis of the quadrature components of narrowband signals (стр. 3 из 3)

Probability distribution laws of the amplitude and phase errors have also been evaluated by the means of computer simulation. For this purpose a LFM signal with time-compression ratio 6 400 was used. Statistical distributions were estimated with usage of 9 600 samples for inphase and 9 600 samples for quadrature components. Thirteen points of these statistical distributions were chosen. The plot of the statistical distribution law

of the phase error values is shown in fig. 5 for various numbers of the A/D converters bits. fig. 6 shows the amplitude error distribution computed for the same case

.

Fig. 5. Probability distribution laws of the phase error for different word length,

Fig. 6. Probability distribution laws of the amplitude error for different word-length,

Conclusion

narrowband signal error

The results of theoretical analysis and computer simulation of the amplitude and phase errors of the narrowband signal, caused by quantizing of the signal's inphase and quadrature components show that the mean of the amplitude of the distorted signals remains equal to the input amplitude, but the output amplitude becomes fluctuated with the variance, determined by the variance of D/A converter error. The phase error has zero mean, maximum deviation 53° and a variance which is inversely proportional to the number of quantization levels. The results achieved may be used in digital filters' design.

references

1. Rabiner, L.R. Theory and Application of Digital Signal Processing / L.R. Rabiner, В. Gold // Englewood Cliffs, NJ. – Prentice-Hall, 2008.

2. Агеев, Р.В. Логарифмическая дискретизация сигналов с заданной абсолютной погрешностью / Р.В. Агеев, Ю.Н. Овчаров // Автометрия. – 2008. – № 6. – С. 23–27.

3. Лифшиц, Н.А.Численные характеристики ошибок квантования амплитуды / Н.А. Лифшиц, В.Е. Фарбер // Автоматика и телемеханика. – 2008. – т. 39, № 12. – с. 176–179.

4. Домрачеев, В.Г. Критерий оценки точности цифровых преобразователей угла / В.Г. Домрачеев, Б.С. Мейко // Измерительная техника. – 2008. – т. 18, № 11. – С. 22–25.

5. Koffler, H. Quantization and roundoff errors in a digital MTI filter, Siemens Forsch. and Entwicklungsber / H. Koffler. – Germany, 2010 – Vol. 2, № 2. – p. 73–78.

6. Snipad, A.B. A necessary and sufficient condition for quantization errors to be uniform and white / A.B. Snipad, D.L. Snyder // IEEE Trans, on Acoust. Speech and Sign. Proc.Vol. – ASSP-25. – 2007. – № 5 (Oct.)–p. 442–448.

7. O'Neal, Iz. Digital encoding of phase shift keying voiceband data signals / Iz. O 'Neal, R.R. Koneru, I.P. Agrawal // Conf. record of Int. Conf. on Acoustics Speech and Signal processing, ICASSP-80. Denver. Co. – 2010. – April 9–11. – P. 315–318.

8. Dvite, G.B. Tables of Integrals and Other Mathematical Data / G.B. Dvite // The Mac Millan Company. – N.Y., 2011. – 634 p.