Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing

Jeffrey Ludwig

doi:doi:10.11648/j.wcmc.20200802.12

| Peer-Reviewed

Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing

Jeffrey Ludwig

Published in International Journal of Wireless Communications and Mobile Computing (Volume 8, Issue 2)

Received: 28 May 2021 Accepted: 15 June 2021 Published: 13 July 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Techniques for reducing power consumption in digital circuits have become increasingly important because of the growing demand for portable multimedia devices. Digital filters, being ubiquitous in such devices, are a prime candidate for low-power design. We present a new algorithmic approach to low-power frequency-selective digital filtering which is based on the concepts of adaptive approximate processing. This approach is formalized by introducing the class of approximate filtering algorithms in which the order of a digital filter is dynamically varied to provide time-varying stopband attenuation in proportion to the time-varying signal-to-noise ratio (SNR) of the input signal, while maintaining a fixed SNR at the filter output. Since power consumption in digital filter implementations is proportional to the order of the filter, dynamically varying the filter order is a strategy which may be used to conserve power. From this practical technique we abstract a theoretical problem which involves the determination of an optimal filter order based on observations of the input data and a set of concrete assumptions on the statistics of the input signal. Two solutions to this theoretical problem are presented, and the key results are used to interpret the solution to the practical low-power filtering problem. We construct a framework to explore the statistical properties of approximate filtering algorithms and show that under certain assumptions, the performance of approximate filtering algorithms is asymptotically optimal.

Published in	International Journal of Wireless Communications and Mobile Computing (Volume 8, Issue 2)
DOI	10.11648/j.wcmc.20200802.12
Page(s)	22-38
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Low-power Signal Processing, Adaptive Filtering, Approximate Signal Processing

References

[1]	Pilipovi´ c, R.; Risojevi´ c, V.; Buli´ c, P. On the Design of an Energy Efficient Digital IIR A-Weighting Filter using Approximate Multiplication. Sensors 2021, 21, 732. https://doi.org/10.3390/s21030732
[2]	M. Kang, S. K. Gonugondla and N. R. Shanbhag, Deep In-Memory Architectures in SRAM: An Analog Approach to Approximate Computing, in Proceedings of the IEEE, vol. 108, no. 12, pp. 2251-2275, Dec. 2020, https://doi.org/10.1109/JPROC.2020.3034117
[3]	Agathoklis, P.; Touil, L.; Hamdi, A.; Gassoumi, I.; Mtibaa, A. Design of Low-Power Structural FIR Filter Using Data-Driven Clock Gating and Multibit Flip-Flops. Journal of Electrical and Computer Engineering 2020 https://doi.org/10.1155/2020/8108591
[4]	Kim, M. S.; Garcia, A. A. D. B.; Oliveira, L. T.; Hermida, R.; Bagherzadeh, N. Efficient Mitchell’s Approximate Log Multipliers for Convolutional Neural Networks. IEEE Trans. Comput. 2018, 68, 660-675.
[5]	Liu, W.; Xu, J.; Wang, D.; Wang, C.; Montuschi, P.; Lombardi, F. Design and Evaluation of Approximate Logarithmic Multipliers for Low Power Error-Tolerant Applications. IEEE Trans. Circuits Syst. I Regul. Pap. 2018, 65, 2856-2868.
[6]	Pilipovi´ c, R.; Buli´ c, P. On the Design of Logarithmic Multiplier Using Radix-4 Booth Encoding. IEEE Access 2020, 8, 64578-64590.
[7]	Leon, V.; Zervakis, G.; Soudris, D.; Pekmestzi, K. Approximate Hybrid High Radix Encoding for Energy- Efficient Inexact Multipliers. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 2018, 26, 421-430.
[8]	Liu, W.; Cao, T.; Yin, P.; Zhu, Y.; Wang, C.; Swartzlander, E.E.; Lombardi, F. Design and Analysis of Approximate Redundant Binary Multipliers. IEEE Trans. Comput. 2019, 68, 804-819.
[9]	Agrawal, A.; Choi, J.; Gopalakrishnan, K.; Gupta, S.; Nair, R.; Oh, J.; Prener, D.A.; Shukla, S.; Srinivasan, V.; Sura, Z. Approximate computing: Challenges and opportunities. In Proceedings of the 2016 IEEE International Conference on Rebooting Computing (ICRC), San Diego, CA, USA, 17-19 October 2016; pp. 1-8.
[10]	Mittal, S. A survey of techniques for approximate computing. ACM Comput. Surv. (CSUR) 2016, 48, 62.
[11]	Jerger, N. E.; Miguel, J. S. Approximate Computing. IEEE Micro 2018, 38, 8-10.
[12]	Eeckhout, L. Approximate Computing, Intelligent Computing. IEEE Micro 2018, 38, 6-7.
[13]	Price M., J. Glass, A. P. Chandrakasan, A Low-Power Speech Recognizer and Voice Activity Detector Using Deep Neural Networks, IEEE Journal of Solid-State Circuits, vol. 53, no. 1, pp. 66-75, Jan. 2018.
[14]	Calhoun, B. H., D. C. Daly, N. Verma, D. Finchelstein, D. D. Wentzloff, A. Wang, S.-H. Cho, and A. P. Chandrakasan, Design Considerations for Ultra-low Energy Wireless Microsensor Nodes, IEEE Transactions on Computers. pp. 727-749, June 2005.
[15]	Tikekar M., V. Sze, A. P. Chandrakasan, A Fully Integrated Energy-Efficient H.265/HEVC Decoder With eDRAM for Wearable Devices, IEEE Journal of Solid- State Circuits, vol. 53, no. 8, pp.2368-2377, Aug. 2018.
[16]	Steiger C., A. Abramson, P. Nadeau, A. P. Chandrakasan, R. Langer, G. Traverso, Ingestible electronics for diagnostics and therapy, Nature Reviews Materials, vol. 4, no. 2, pp. 83-98, Dec. 2018.
[17]	Mimee M., P. Nadeau, A. Hayward, S. Carim, S. Flanagan, L. Jerger, J. Collins, S. McDonnell, R. Swartwout, R. J. Citorik, V. Bulovic, R. Langer, G. Traverso, A. P. Chandrakasan, T. K. Lu, An ingestible bacterial-electronic system to monitor gastrointestinal health, Science, vol. 360, no. 6391, pp. 915-918, May 2018.
[18]	Banerjee U., A. Wright, C. Juvekar, M. Waller, Arvind, A. P. Chandrakasan, An Energy-Efficient Reconfigurable DTLS Cryptographic Engine for Securing Internet- of-Things Applications, IEEE Journal of Solid-State Circuits, vol. 54, no. 8, pp. 2339-2352, Aug. 2019.
[19]	J. T. Ludwig, S. H. Nawab, and A. P. Chandrakasan. Convergence results on adaptive approximate filtering. In Advanced Signal Processing Algorithms (F. T. Luk, ed.), Proceedings of SPIE, Denver, CO, August 1996.
[20]	J. T. Ludwig, S. H. Nawab, and A. P. Chandrakasan. Low- power digital filtering using approximate processing. IEEE Journal on Solid State Circuits, 31 (3): 395-400, March 1996.
[21]	J. T. Ludwig. Low-power Digital Filtering Using Adaptive Approximate Processing. Ph.D. Thesis, Department of Electrical Engineering and Computer Science, MIT RLE. September 2, 1997.
[22]	C. J. Pan. A Low-power digital filter for decimation and interpolation using approximate processing. International Solid State Circuits Conference, pages 102-103, February, 1997.
[23]	E. Lee and D. G. Messerschmitt. Digital Communication. Kluwer Academic Publishers, Boston, MA, 1994.
[24]	G. A. Ghazal. Moments of the ratio two dependent quadratic forms. Statistics and Probability Letters, 20 (4): 313-315, 1994.
[25]	Lieberman. Saddlepoint approximation for the distribution of a ratio of quadratic forms in normal variables. Journal of the American Statistical Association, 89 (427): 924-928, 1994.
[26]	M. D. Smith. Expectations of ratios of quadratic forms. Journal of Multivariate Analysis, 31: 244-257, 1989.
[27]	M. D. Smith. Comparing approximations to the expectation of a ratio of quadratic forms in normal variables. Econometric Reviews, 15 (1): 81-95, 1996.
[28]	L. L. Scharf. Statistical Signal Processing: Detection, Estimation, and Time Series Analysis. Addison-Wesley Publishing Company, Reading, MA, 1991.
[29]	S. M. Kay. Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, Upper Saddle River, NJ, 1993.
[30]	S. M. Kay. Modern Spectrum Estimation: Theory and Application. Prentice Hall, Englewood Cliffs, NJ, 1988.
[31]	Boaz Porat. Digital Processing of Random Signals: Theory and Methods. Prentice Hall, Englewood Cliffs, NJ, 1994.
[32]	Padmapriya, S.; Lakshmi Prabha, V. Design of an efficient dual mode reconfigurable FIR filter architecture in speech signal processing, Microprocessors and Microsystems, 2015 39, 7, 521-528.

Cite This Article

Plain Text BibTeX RIS

APA Style

Jeffrey Ludwig. (2021). Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing. International Journal of Wireless Communications and Mobile Computing, 8(2), 22-38. https://doi.org/10.11648/j.wcmc.20200802.12

Copy | Download

ACS Style

Jeffrey Ludwig. Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing. Int. J. Wirel. Commun. Mobile Comput. 2021, 8(2), 22-38. doi: 10.11648/j.wcmc.20200802.12

Copy | Download

AMA Style

Jeffrey Ludwig. Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing. Int J Wirel Commun Mobile Comput. 2021;8(2):22-38. doi: 10.11648/j.wcmc.20200802.12

Copy | Download

@article{10.11648/j.wcmc.20200802.12,
  author = {Jeffrey Ludwig},
  title = {Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing},
  journal = {International Journal of Wireless Communications and Mobile Computing},
  volume = {8},
  number = {2},
  pages = {22-38},
  doi = {10.11648/j.wcmc.20200802.12},
  url = {https://doi.org/10.11648/j.wcmc.20200802.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wcmc.20200802.12},
  abstract = {Techniques for reducing power consumption in digital circuits have become increasingly important because of the growing demand for portable multimedia devices. Digital filters, being ubiquitous in such devices, are a prime candidate for low-power design. We present a new algorithmic approach to low-power frequency-selective digital filtering which is based on the concepts of adaptive approximate processing. This approach is formalized by introducing the class of approximate filtering algorithms in which the order of a digital filter is dynamically varied to provide time-varying stopband attenuation in proportion to the time-varying signal-to-noise ratio (SNR) of the input signal, while maintaining a fixed SNR at the filter output. Since power consumption in digital filter implementations is proportional to the order of the filter, dynamically varying the filter order is a strategy which may be used to conserve power. From this practical technique we abstract a theoretical problem which involves the determination of an optimal filter order based on observations of the input data and a set of concrete assumptions on the statistics of the input signal. Two solutions to this theoretical problem are presented, and the key results are used to interpret the solution to the practical low-power filtering problem. We construct a framework to explore the statistical properties of approximate filtering algorithms and show that under certain assumptions, the performance of approximate filtering algorithms is asymptotically optimal.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing
AU  - Jeffrey Ludwig
Y1  - 2021/07/13
PY  - 2021
N1  - https://doi.org/10.11648/j.wcmc.20200802.12
DO  - 10.11648/j.wcmc.20200802.12
T2  - International Journal of Wireless Communications and Mobile Computing
JF  - International Journal of Wireless Communications and Mobile Computing
JO  - International Journal of Wireless Communications and Mobile Computing
SP  - 22
EP  - 38
PB  - Science Publishing Group
SN  - 2330-1015
UR  - https://doi.org/10.11648/j.wcmc.20200802.12
AB  - Techniques for reducing power consumption in digital circuits have become increasingly important because of the growing demand for portable multimedia devices. Digital filters, being ubiquitous in such devices, are a prime candidate for low-power design. We present a new algorithmic approach to low-power frequency-selective digital filtering which is based on the concepts of adaptive approximate processing. This approach is formalized by introducing the class of approximate filtering algorithms in which the order of a digital filter is dynamically varied to provide time-varying stopband attenuation in proportion to the time-varying signal-to-noise ratio (SNR) of the input signal, while maintaining a fixed SNR at the filter output. Since power consumption in digital filter implementations is proportional to the order of the filter, dynamically varying the filter order is a strategy which may be used to conserve power. From this practical technique we abstract a theoretical problem which involves the determination of an optimal filter order based on observations of the input data and a set of concrete assumptions on the statistics of the input signal. Two solutions to this theoretical problem are presented, and the key results are used to interpret the solution to the practical low-power filtering problem. We construct a framework to explore the statistical properties of approximate filtering algorithms and show that under certain assumptions, the performance of approximate filtering algorithms is asymptotically optimal.
VL  - 8
IS  - 2
ER  -

Copy | Download

Author Information

Jeffrey Ludwig

Department of Mathematics, University of California, Irvine, United States of America

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Jeffrey Ludwig. (2021). Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing. International Journal of Wireless Communications and Mobile Computing, 8(2), 22-38. https://doi.org/10.11648/j.wcmc.20200802.12

Copy | Download

ACS Style

Jeffrey Ludwig. Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing. Int. J. Wirel. Commun. Mobile Comput. 2021, 8(2), 22-38. doi: 10.11648/j.wcmc.20200802.12

Copy | Download

AMA Style

Jeffrey Ludwig. Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing. Int J Wirel Commun Mobile Comput. 2021;8(2):22-38. doi: 10.11648/j.wcmc.20200802.12

Copy | Download

@article{10.11648/j.wcmc.20200802.12,
  author = {Jeffrey Ludwig},
  title = {Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing},
  journal = {International Journal of Wireless Communications and Mobile Computing},
  volume = {8},
  number = {2},
  pages = {22-38},
  doi = {10.11648/j.wcmc.20200802.12},
  url = {https://doi.org/10.11648/j.wcmc.20200802.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wcmc.20200802.12},
  abstract = {Techniques for reducing power consumption in digital circuits have become increasingly important because of the growing demand for portable multimedia devices. Digital filters, being ubiquitous in such devices, are a prime candidate for low-power design. We present a new algorithmic approach to low-power frequency-selective digital filtering which is based on the concepts of adaptive approximate processing. This approach is formalized by introducing the class of approximate filtering algorithms in which the order of a digital filter is dynamically varied to provide time-varying stopband attenuation in proportion to the time-varying signal-to-noise ratio (SNR) of the input signal, while maintaining a fixed SNR at the filter output. Since power consumption in digital filter implementations is proportional to the order of the filter, dynamically varying the filter order is a strategy which may be used to conserve power. From this practical technique we abstract a theoretical problem which involves the determination of an optimal filter order based on observations of the input data and a set of concrete assumptions on the statistics of the input signal. Two solutions to this theoretical problem are presented, and the key results are used to interpret the solution to the practical low-power filtering problem. We construct a framework to explore the statistical properties of approximate filtering algorithms and show that under certain assumptions, the performance of approximate filtering algorithms is asymptotically optimal.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Asymptotically Optimal Low-Power Digital Filtering Using Adaptive Approximate Processing
AU  - Jeffrey Ludwig
Y1  - 2021/07/13
PY  - 2021
N1  - https://doi.org/10.11648/j.wcmc.20200802.12
DO  - 10.11648/j.wcmc.20200802.12
T2  - International Journal of Wireless Communications and Mobile Computing
JF  - International Journal of Wireless Communications and Mobile Computing
JO  - International Journal of Wireless Communications and Mobile Computing
SP  - 22
EP  - 38
PB  - Science Publishing Group
SN  - 2330-1015
UR  - https://doi.org/10.11648/j.wcmc.20200802.12
AB  - Techniques for reducing power consumption in digital circuits have become increasingly important because of the growing demand for portable multimedia devices. Digital filters, being ubiquitous in such devices, are a prime candidate for low-power design. We present a new algorithmic approach to low-power frequency-selective digital filtering which is based on the concepts of adaptive approximate processing. This approach is formalized by introducing the class of approximate filtering algorithms in which the order of a digital filter is dynamically varied to provide time-varying stopband attenuation in proportion to the time-varying signal-to-noise ratio (SNR) of the input signal, while maintaining a fixed SNR at the filter output. Since power consumption in digital filter implementations is proportional to the order of the filter, dynamically varying the filter order is a strategy which may be used to conserve power. From this practical technique we abstract a theoretical problem which involves the determination of an optimal filter order based on observations of the input data and a set of concrete assumptions on the statistics of the input signal. Two solutions to this theoretical problem are presented, and the key results are used to interpret the solution to the practical low-power filtering problem. We construct a framework to explore the statistical properties of approximate filtering algorithms and show that under certain assumptions, the performance of approximate filtering algorithms is asymptotically optimal.
VL  - 8
IS  - 2
ER  -

Copy | Download