Mathematical Modeling of Sampling, Quantization, and Coding in Sigma Delta Converter using Matlab

  • Azeez Abdullah Azeez Barzinjy Department of Physics, College of Education, Salahaddin University-Erbil, Kurdistan Region - Iraq
  • Haidar Jalal Ismail Department of Physics, College of Education, Salahaddin University-Erbil, Zanko, Erbil, Iraq
  • Mudhaffer Mustafa Ameen Department of Physics, College of Education, Salahaddin University-Erbil, Zanko, Erbil, Iraq


The received analog signal must be digitized before the digital signal processing can demodulate it. Sampling, quantization, and coding are the separate stages for the analog-to-digital adaptation procedure. The procedure of adapting an unceasing time-domain signal into a separate time-domain signal is called sampling. While, the procedure of adapting a separate-time, continuous-valued signal into a discrete-time, discrete-valued signal is known as quantization. Thus, quantization error is the mismatch between the unquantized sample and the quantized sample. The method of demonstrating the quantized samples in binary form is known as coding. This investigation utilized Matlab® program to recommend a proper scheme for a wireless-call button network of input signal, normalized frequency, and over-sampling ratio against signal-to-quantization noise ratio. Two vital characteristics of this wireless network design are cost-effective and low-power utilization. This investigation, through reducing the in-band quantization error, also studied how oversampling can enhance the accomplishment of an analog-to-digital adapter.

Index Terms: Analog-to-digital Adapter, Coding, Matlab, Quantization Error, Wireless Network


[1] W. A. Kester. “Analog devices,” in Data Conversion Handbook, Burlington, MA: Elsevier, 2005.

[2] K. Fowler. “Part 7: Analog-to-digital conversion in real-time systems.” IEEE Instrumentation and Measurement Magazine, vol. 6, No. 3, pp. 58-64, 2003.

[3] R. Schreier and G. C. Temes. Understanding Delta-Sigma Data Converters, vol. 74. Piscataway, NJ: IEEE Press, 2005.

[4] J. M. de la Rosa and R. Río. CMOS Sigma-Delta Converters: Practical Design Guide, Hoboken, NJ: Wiley, 2013.

[5] M. Pelgrom. Analog-to-Digital Conversion, Switzerland: Springer International Publishing, 2016.

[6] J. Keyzer, J. Hinrichs, A. Metzger, M. Iwamoto, I. Galton and P. Asbeck. “Digital generation of RF signals for wireless communications with band-pass delta-sigma modulation.” in Microwave Symposium Digest, IEEE MTT-S International, 2001.

[7] J. J. Wikner and N. Tan. “Modeling of CMOS digital-to-analog converters for telecommunication.” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 46, no. 5, pp. 489-499, 1999.

[8] J. Kim, T. K. Jang and Y. G. Yoon. “Analysis and design of voltage-controlled oscillator based analog-to-digital converter.” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 1, pp. 18-30, 2010.

[9] B. S. Song. MicroCMOS Design, Hoboken, NJ: Taylor & Francis, 2011.

[10] J. G. Proakis and D. G. Manolakis. Digital Signal Processing: Principles, Algorithms, and Applications, New Jersey, USA: Prentice Hall, 1996.

[11] G. J. Foschini and M. J. Gans. “On limits of wireless communications in a fading environment when using multiple antennas.” Wireless Personal Communications, vol. 6, no. 3, pp. 311-335, 1998.

[12] K. Sudakshina. Analog and Digital Communications, Singapore: Pearson Education India, 2010.

[13] J. S. Chitode. Principles of Communication, Pune: Technical Publications, 2009.

[14] D. R. Morgan, Z. Ma, J. S. Kenney, J. Kim and C. R. Giardina. “A generalized memory polynomial model for digital predistortion of RF power amplifiers.” IEEE Transactions on Signal Processing, vol. 54, no. 10, pp. 3852-3860, 2006.

[15] B. Le, T. W. Rondeau, J. H. Reed and C. W. Bostian. “Analog-to-digital converters.” IEEE Signal Processing Magazine, vol. 22, no. 6. pp. 69-77, 2005.

[16] S. K. Mitra and S. K. Mitra. Digital Signal Processing: A Computer-based Approach, New York: McGraw-Hill, 2011.

[17] V. Mladenov, P. Karampelas, G. Tsenov and V. Vita. “Approximation formula for easy calculation of signal-to-noise ratio of sigma-delta modulators.” ISRN Signal Processing, vol. 2011, Article ID: 731989. pp. 7, 2011.

[18] K. Francken and G. G. Gielen. “A high-level simulation and synthesis environment for/spl Delta//spl Sigma/modulators.” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 22, no. 8. p. 1049-1061, 2003.

[19] B. E. Bammes, R. H. Rochat, J. Jakana, D. H. Chen and W. Chiu. “Direct electron detection yields cryo-EM reconstructions at resolutions beyond 3/4 Nyquist frequency.” Journal of Structural Biology, vol. 177, no. 3, p. 589-601, 2012.

[20] A. Belitski, A. Gretton, C. Magri, Y. Murayama, M. A. Montemurro, N. K. Logothetis, S. Panzeri. “Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information.” Journal of Neuroscience, vol. 28, no. 22, pp. 5696-5709, 2008.

[21] F. Overney, A. Rufenacht, J. P. Braun and B. Jeanneret. “Josephson-based test bench for ac characterization of analog-to-digital converters.” in Precision Electromagnetic Measurements (CPEM), 2010 Conference on IEEE, 2010.

[22] A. Posselt, D. Berges, O. Klemp, B. Geck. “Design and evaluation of frequency-agile multi-standard direct RF digitizing receivers for automotive use.” in Vehicular Technology Conference (VTC Spring), IEEE 81st, IEEE, 2015.

[23] P. M. Aziz, H. V. Sorensen and J. van der Spiegel. “An overview of sigma-delta converters.” IEEE Signal Processing Magazine, vol. 13, no. 1, pp. 61-84, 1996.

[24] T. L. Brooks, D. H. Robertson, D. F. Kelly, A. Del Muro and S. W. Harston. “A cascaded sigma-delta pipeline A/D converter with 1.25 MHz signal bandwidth and 89 dB SNR.” IEEE Journal of Solid-State Circuits, vol. 32, no. 12, pp. 1896-1906, 1997.

[25] I. Fujimori, L. Longo, and A. Hirapethian. “A 90-dB SNR 2.5-MHz output-rate ADC using cascaded multibit delta-sigma modulation at 8/spl times/oversampling ratio.” IEEE Journal of Solid-State Circuits, vol. 35. no. 12. pp. 1820-1828, 2000.
How to Cite
BARZINJY, Azeez Abdullah Azeez; ISMAIL, Haidar Jalal; AMEEN, Mudhaffer Mustafa. Mathematical Modeling of Sampling, Quantization, and Coding in Sigma Delta Converter using Matlab. UHD Journal of Science and Technology, [S.l.], v. 1, n. 1, p. 17-22, apr. 2017. ISSN 2521-4217. Available at: <>. Date accessed: 16 june 2021. doi:

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