Skip to main content
SpringerLink
Log in

Sampling

  • Chapter
Analog-to-Digital Conversion

  • 2673 Accesses

Abstract

Sampling is one of the main processes in an analog-to-digital converter. The sampling theory is examined and the crucial elements are extensively discussed. The relation with other techniques, such as modulation and sampling of noise is described.

The second section discusses the design of time-discrete filters. These filters form an important building block in several conversion structures especially in sigma-delta conversion. Down-sample filters transform the bit-stream format into a more usable pulse-code format. The essential properties of Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters are reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Strange in the sense that many normal mathematical operations cannot be performed, e.g. δ 2(t) does not exist.

  2. 2.

    To keep in this section time-continuous and sampled sequences and their spectra apart, time domain signals use normal print, while their spectral equivalents use bold face. The suffix s refers to sample sequences.

  3. 3.

    The only storage in the early days of CDs were video recorders. The 44.1 ks/s sample rate was chosen such that the audio signal exactly fits to a PAL video recorder format (25 fields of 588 lines with 3 samples per line) of 44.1 ks/s.

  4. 4.

    A peak-peak value is often used for jitter, but peak-peak values for stochastic processes have no significance if the process and the corresponding number of observations is not identified.

  5. 5.

    The human ear is sensitive for delay variations in sound.

  6. 6.

    The definition for Euler’s relation is: e jπ+1=0. According to Feynman this is the most beautiful mathematical formula as it is relates the most important mathematical constants to each other.

  7. 7.

    An equivalent analog filter would require 10–12 poles.

  8. 8.

    In the period 1970–1980 the charge-coupled device was seen as a promising candidate for storage, image sensing and signal processing. Analog charge packets are in this multi-gate transistor shifted, split and joint along the surface of the semiconductor. Elegant, but not robust enough to survive the digital era.

Bibliography

3 Sampling

  1. L.R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice Hall, Inc., Englewood Cliffs, 1975), ISBN: 0-139-141014

    Google Scholar 

  2. A.W.M. van den Enden, N.A.M. Verhoeckx, Discrete Time Signal Processing, an Introduction (Prentice Hall, New York, 1989), ISBN: 0-132-167557

    Google Scholar 

  3. H. Nyquist, Certain topics in telegraph transmission theory. Transactions of the AIEE 47, 617–644 (1928), reprinted in Proceedings of the IEEE 90, 280–305 (2002)

    Google Scholar 

  4. C.E. Shannon, A mathematical theory of communication. The Bell System Technical Journal 27, 379–423 and 623–656 (1948)

    MathSciNet  MATH  Google Scholar 

  5. C.E. Shannon, Communication in the presence of noise, Proceedings of the IRE, pp. 10–21 (1949), reprinted in Proceedings of the IEEE 86, 447–457 (1998)

    Google Scholar 

  6. M. Unser, Sampling-50 years after Shannon. Proceedings of the IEEE 88, 569–587 (2000)

    Article  Google Scholar 

  7. E. Candes, J. Romberg, T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory 52, 489–509 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Shinagawa, Y. Akazawa, T. Wakimoto, Jitter analysis of high-speed sampling systems. IEEE Journal of Solid-State Circuits 25, 220–224 (1990)

    Article  Google Scholar 

  9. J.H. McClellan, T.W. Parks, L.R. Rabiner, A computer program for designing optimum FIR linear phase digital filters. IEEE Transactions on Audio Electroacoustics 21, 506–526 (1973)

    Article  Google Scholar 

  10. C.H. Séquin, M.F. Tompsett, Charge Transfer Devices (Academic Press, New York, 1975), Supplement 8 to Advances in Electronics and Electron Physics

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NXP Semiconductors, HTC-32, Eindhoven, 5656AE, The Netherlands

    Marcel J. M. Pelgrom

Authors
  1. Marcel J. M. Pelgrom
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcel J. M. Pelgrom .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Pelgrom, M.J.M. (2010). Sampling. In: Analog-to-Digital Conversion. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8888-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-8888-8_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8887-1

  • Online ISBN: 978-90-481-8888-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation