A Mathematical Model for Signal’s Energy at the Output of an Ideal DAC

Paola Loreti, Pierluigi Vellucci

2016

Abstract

The presented research work considers a mathematical model for energy of the signal at the output of an ideal DAC, in presence of sampling clock jitter. When sampling clock jitter occurs, the energy of the signal at the output of ideal DAC does not satisfies a Parseval identity. Nevertheless, an estimation of the signal energy is here shown by a direct method involving sinc functions.

References

  1. Abidi, A. (2006). Phase noise and jitter in CMOS ring oscillators. IEEE J. Solid-State Circuits, 41:1803-1816.
  2. Alegria, F. and Serra, A. (2010). Gaussian jitter-induced bias of sine wave amplitude estimation using threeparameter sine fitting. Instrumentation and Measurement, IEEE Transactions on, 59:2328-2333.
  3. Angrisani, L., D'Apuzzo, P., and D'Arco, M. (2009). Modeling timing jitter effects in digital-to-analog converters. IEEE Trans. Instrum. Meas, 58:330-336.
  4. Corradini, L., Bjeletic, A., Zane, R., and Maksimovic, D. (2011). Fully Digital Hysteretic Modulator for DCDC Switching Converters. IEEE Trans. on Power Electronics, 26:2969-2979.
  5. D'Apuzzo, M., D'Arco, M., Liccardo, A., and Vadursi, M. (2010). Modeling DAC Output Waveforms. IEEE Trans. Instrum. Meas, 59:2854-2862.
  6. Demir, A., Mehrotra, A., and Roychowdhury, J. (2000). Phase noise in oscillators: a unifying theory and numerical methods for characterization. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 47:655-674.
  7. Guo, Y., Zhang, Z., Hui, Z., Zeng, X., and Cheng, X. (2014). First Order Analytical Model for Deterministic Jitter in Digital-to-Analogue Converters. Information Science and System Science.
  8. Hajimiri, A. and Lee, T. (1998). A general theory of phase noise in electrical oscillators. IEEE J. Solid-State Circuits, 33:179-194.
  9. Hellinger, E. and Toeplitz, O. (1910). Grundlagen fur eine Theorie der unendlichen Matrizen. Mathematische Annalen, 69:289-330.
  10. Ingham, A. E. (1936). Some Trigonometrical Inequalities with Applications to the Theory of Series. Math. Z., 41:367-379.
  11. Kurosawa, N. (2002). Sampling clock jitter effects in digital-to-analog converters. Measurement, 31:187- 199.
  12. Manolakis, D. G. and Ingle, V. K. (2011). Applied digital signal processing: theory and practice. Cambridge University Press.
  13. Montgomery, H. L. and Vaughan, R. C. (1974). Hilbert's inequality. J. London Math. Soc., 8:73-82.
  14. Razavi, B. (1996). A study of phase noise in CMOS oscillators. IEEE J. Solid-State Circuits, 31:331-343.
  15. Reinhardt, V. S. (2005). A review of time jitter and digital systems. In Proceedings of the 2005 IEEE International Frequency Control Symposium and Expositio, pages 38-45.
  16. Schur, I. (1911). Bemerkungen zur Theorie der beschrankten Bilinearformen mit unendlich vielen Veranderlichen. J. Reine Angew. Math., 140:1-28.
  17. Shi, Q., Gong, Y., and Guan, Y. L. (2008). Asynchronous classification of high-order qams. InWireless Communications and Networking Conference, 2008. WCNC 2008. IEEE, pages 1188-1193.
  18. Tatsis, G., Votis, C., Raptis, V., Christofilakis, V., and Kostarakis, P. (2010). A/D restrictions (errors) in Ultra-Wideband Impulse Radios. Int. J. Communications, Network and System Sciences,, 3:425-429.
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Paper Citation


in Harvard Style

Loreti P. and Vellucci P. (2016). A Mathematical Model for Signal’s Energy at the Output of an Ideal DAC . In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-198-4, pages 347-352. DOI: 10.5220/0005979303470352


in Bibtex Style

@conference{icinco16,
author={Paola Loreti and Pierluigi Vellucci},
title={A Mathematical Model for Signal’s Energy at the Output of an Ideal DAC},
booktitle={Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2016},
pages={347-352},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005979303470352},
isbn={978-989-758-198-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - A Mathematical Model for Signal’s Energy at the Output of an Ideal DAC
SN - 978-989-758-198-4
AU - Loreti P.
AU - Vellucci P.
PY - 2016
SP - 347
EP - 352
DO - 10.5220/0005979303470352