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Quantization

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Analog-to-Digital Conversion

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Abstract

Quantization is the second main process in conversion. This chapter deals with the mathematical derivation of quantization in several resolution ranges. Quantization results in several specific parameters: integral and differential linearities and derived problems such as monotonicity.The signal-to-noise ratio is also affected by quantization. Some special topics are the effect of dither and the relation between differential non-linearity and signal-to-noise.

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Notes

  1. 1.

    Other coding schemes will appear when discussing the implementation of complex converters, e.g., locally ternary (three-level) coding can be used in full differential implementations. In error correction schemes a base lower than 2 is applied.

  2. 2.

    The IEEE has standardized a number of conversion terms in standards IEEE 1057 [48] and IEEE 1241 [49, 50].

  3. 3.

    Other binary code formats are discussed in Sect. 7.1.1

  4. 4.

    N. Blachman has mathematically analyzed many processes around quantization. His publications from 1960–1985 form a good starting point to dive deeper in this field, e.g., [52].

  5. 5.

    Note that in a formal sense just voltage-squared is calculated, which lacks the impedance level and the time span needed to reach the dimension of power: Watt or V2/\(\Omega \) s. In quantization theory “voltage-squared” power is only used to compare to another “voltage-squared” power, assuming that both relate to the same impedance level and the same time span. This quantization error becomes visible to an engineer (mostly) as part of a power spectrum. For that reason this book prefers the term quantization power instead of energy.

  6. 6.

    43.8 dB is a short hand for 4. 167 × 10−5 power ratio. Use the exponential notation in complex calculations.

  7. 7.

    There has been an extensive search for optimum dither signals in the 1960–1970s. After that era the interest for dither has reduced. The concept, however, still provides valuable insight, e.g., sigma-delta converters can be understood as low-resolution converters that generate their own dither.

  8. 8.

    A manipulation like this is aversely coined: “specmanship.”

  9. 9.

    Non-English speakers often confuse monotonic with monotonous which is synonymous to boring, dull, and uninteresting.

  10. 10.

    The author of this book was educated with the notion that “log” operations can only be performed on dimensionless quantities. Obviously this is not the case here.

  11. 11.

    Compared to Moore’s law for digital circuit where speed doubles and area and power halves for every generation (2 years) this is a meager result.

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  1. HELMOND, Noord-Brabant, The Netherlands

    Marcel Pelgrom

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Pelgrom, M. (2017). Quantization. In: Analog-to-Digital Conversion. Springer, Cham. https://doi.org/10.1007/978-3-319-44971-5_4

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  • DOI: https://doi.org/10.1007/978-3-319-44971-5_4

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