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Cited by 168Digital Filter Design and ImplementationAdvanced Adaptive Filtering TechniquesAnalog and Mixed-Signal Circuit Design

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Roundoff noise in digital filters: Frequency transformations and invariants

Mullis, C., Roberts, R.·1976·IEEE Transactions on Acoustics, Speech, and Signal Processing
DOI 10.1109/tassp.1976.1162869
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Abstract

The family of filters {H(F(z)):F(z) a frequency transformation} generated from a prototype filter H(z) is shown to possess certain common properties. These are coordinate-free quantities (called second-order modes) which are invariant under frequency transformation. The invariance is significant in the design of low-noise fixed-point digital filter structures since the second-order modes characterize the minimum attainable noise. Filter structures (including parallel, cascade, and ladder configurations) are studied whose output noise is essentially independent of bandwidth and center frequency. An analysis of direct form structures (whether isolated or as one section within a cascade or parallel configuration) results in an expression giving the dominant term in the output noise as a function of the parameter in the low-pass-low-pass transformation. This noise term approaches infinity as bandwidth approaches zero. Thus, for narrowband filters, a difference of several orders of magnitude in the output noise can exist between a scaled direct form (having six multiplications per two-pole section) and the optimal form (having nine multiplications per two-pole section).

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Research works printed but not linked: 16

  1. 10.1109/TCS.1974.1083865 · DOI
  2. lapp, 1974, Some Useful Algorithms for the Analysis of Multiplier Round-Off Noise in Cascade Digital Filters
  3. 10.1109/TCS.1974.1083783 · DOI
  4. liu, 1975, Heuristic optimization of the cascade realization of fixed-point digital filters, IEEE Trans Acoust Speech Signal Processing, assp 23, 464
  5. hwang, 1976, Minimum unit noise in the state space digital filtering, Proc Acoust Speech Signal Process
  6. bellman, 1960, Introduction to Matrix Analysis
  7. kalman, 1969, Topics in Mathematical System Theory, 43
  8. 10.1049/piee.1970.0281 · DOI
  9. 10.1109/TASSP.1975.1162724 · DOI
  10. 10.1016/j.sigpro.2007.12.009 · DOI
  11. oppenheim, 1975, Digital Signal Processing, 226
  12. kaiser, 1965, Some Practical Considerations in the Realization of Linear Digital Filters, Proc 3rd Allerton Conf Circuit and System Theory, 621
  13. 10.1109/TCS.1976.1084254 · DOI
  14. 10.1109/TASSP.1975.1162680 · DOI · Paper page
  15. 10.1109/TAU.1973.1162522 · DOI
  16. 10.1109/TAU.1970.1162084 · DOI

Cited by

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Metadata

Authors
Mullis, C., & Roberts, R.
Affiliations
University of Colorado Boulder (US)
ORCID
Roberts, R.
Venue
IEEE Transactions on Acoustics, Speech, and Signal Processing
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
1976-12
Volume
24
Issue
6
Pages
538-550
ISSN
0096-3518 (ISSN-L)
DOI
10.1109/tassp.1976.1162869
OpenAlex
W1976360164
Cited by
168
References
0
Citations by year
2022: 5 · 2021: 3 · 2020: 1 · 2019: 1 · 2018: 2 · 2017: 1 · 2016: 5 · 2015: 2 · 2014: 3 · 2013: 7 · 2012: 1
FWCI
3.56
Type
journal article
Language
en
Open access
closed
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
Locations
IEEE Transactions on Acoustics Speech and Signal Processing (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
  • Physical Sciences › Computer Science › Signal Processing › Advanced Adaptive Filtering Techniques
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Analog and Mixed-Signal Circuit Design
Keywords
roundoff noise, digital filters, frequency transformation, second-order mode, invariants, direct-form structure, ladder filters, narrowband filters, output noise

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CoChat. (2026). Citation check: Roundoff noise in digital filters: Frequency transformations and invariants. https://app.cochat.ai/papers/10.1109/tassp.1976.1162869
The paper
Mullis, C., & Roberts, R. (1976). Roundoff noise in digital filters: Frequency transformations and invariants. IEEE Transactions on Acoustics, Speech, and Signal Processing. https://doi.org/10.1109/tassp.1976.1162869