Audiogram matching in hearing aid using approximate arithmetic


Filter banks are the major signal processing blocks that dissipate large amount of power in a portable digital hearing aid device. The power consumption can be reduced by replacing the power-hungry multipliers of the filter by power efficient approximate multipliers. This paper illustrates the application of an approximate multiplier for error tolerant hearing aid application. Frequency response masking approach is used for the development of a 10-band non-uniform approximate FIR filter bank with a minimum stop band attenuation of greater than 50 dB. Audiogram matching is done with audiograms of different types of moderate hearing loss and the matching error is computed. Simulation results show that the audiogram matching error falls within +/− 5 dB range.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. Baugh, C. R., & Wooley, B. A. (1973). A two’s complement parallel array multiplication algorithm. IEEE Transactions on Computers, 100(12), 1045–1047

    Article  Google Scholar 

  2. Bornholt, J., Mytkowicz, T., & McKinley, K. S. (2015). Uncertaint: Abstractions for uncertain hardware and software. IEEE Micro, 35(3), 132–143

    Article  Google Scholar 

  3. Chippa, V. K., Mohapatra, D., Raghunathan, A., Roy, K., & Chakradhar, S. T. (2010). Scalable effort hardware design: Exploiting algorithmic resilience for energy efficiency. In Design automation conference (pp. 555–560). IEEE.

  4. Deng, T. B. (2010). Three-channel variable filter-bank for digital hearing aids. IET Signal Processing, 4(2), 181–196

    Article  Google Scholar 

  5. Garofalo, V., Petra, N., De Caro, D., Strollo, A. G., & Napoli, E. (2008). Low error truncated multipliers for DSP applications. In 2008 15th IEEE international conference on electronics, circuits and systems (pp. 29–32). IEEE.

  6. Gupta, V., Mohapatra, D., Raghunathan, A., & Roy, K. (2012). Low-power digital signal processing using approximate adders. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 32(1), 124–137

    Article  Google Scholar 

  7. Gustafsson, O., Johansson, H., and Wanhammar, L. (2000). Design and efficient implementation of narrow-band single filter frequency masking FIR filters. In 2000 10th European signal processing conference (pp. 1–4). IEEE.

  8. Gustafsson, O., Johansson, H., & Wanhammar, L. (2001). Narrow-band and wide-band single filter frequency masking FIR filters. In ISCAS 2001. The 2001 IEEE international symposium on circuits and systems (Cat. No. 01CH37196) (Vol. 2, pp. 181–184). IEEE.

  9. Haridas, N., & Elias, E. (2016). Efficient variable bandwidth filters for digital hearing aid using Farrow structure. Journal of Advanced Research., 7(2), 255–262

    Article  Google Scholar 

  10. Hashemi, S., Bahar, R. I., & Reda, S. (2015). DRUM: A dynamic range unbiased multiplier for approximate applications. In 2015 IEEE/ACM international conference on computer-aided design (ICCAD) (pp. 418–425). IEEE.

  11. Jiang, H., Han, J., Qiao, F., & Lombardi, F. (2015). Approximate radix-8 booth multipliers for low-power and high-performance operation. IEEE Transactions on Computers, 65(8), 2638–2644

    MathSciNet  Article  Google Scholar 

  12. Jiang, H., Liu, C., Liu, L., Lombardi, F., & Han, J. (2017). A review, classification, and comparative evaluation of approximate arithmetic circuits. ACM Journal on Emerging Technologies in Computing Systems (JETC), 13(4), 1–34

    Article  Google Scholar 

  13. Jiang, H., Santiago, F. J., Ansari, M. S., Liu, L., Cockburn, B. F., Lombardi, F., & Han, J. (2019). Characterizing approximate adders and multipliers optimized under different design constraints. In Proceedings of the 2019 on great lakes symposium on VLSI (pp. 393–398).

  14. Jouppi, N. P., Young, C., Patil, N., Patterson, D., Agrawal, G., Bajwa, R., Bates, S., Bhatia, S., Boden, N., Borchers, A., & Boyle, R. (2017). In-datacenter performance analysis of a tensor processing unit. In Proceedings of the 44th annual international symposium on computer architecture (pp. 1–12).

  15. Kulkarni, P., Gupta, P., & Ercegovac, M. (2011). Trading accuracy for power with an underdesigned multiplier architecture. In 2011 24th international conference on VLSI design (pp. 346–351). IEEE.

  16. Leon, V., Zervakis, G., Soudris, D., & Pekmestzi, K. (2017). Approximate hybrid high radix encoding for energy-efficient inexact multipliers. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 26(3), 421–430

    Article  Google Scholar 

  17. Lian, Y., & Wei, Y. (2005). A computationally efficient nonuniform FIR digital filter bank for hearing aids. IEEE Transactions on Circuits and Systems i: Regular Papers, 52(12), 2754–2762

    Article  Google Scholar 

  18. Lim, Y. (1986). Frequency-response masking approach for the synthesis of sharp linear phase digital filters. IEEE Transactions on Circuits and Systems, 33(4), 357–364

    Article  Google Scholar 

  19. Lim, Y. C., & Lian, Y. (1993). The optimum design of one-and two-dimensional FIR filters using the frequency response masking technique. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 40(2), 88–95

    Article  Google Scholar 

  20. Liu, W., Lombardi, F., & Shulte, M. (2020). A retrospective and prospective view of approximate computing [point of view]. Proceedings of the IEEE, 108(3), 394–399

    Article  Google Scholar 

  21. Liu, W., Qian, L., Wang, C., Jiang, H., Han, J., & Lombardi, F. (2017). Design of approximate radix-4 booth multipliers for error-tolerant computing. IEEE Transactions on Computers, 66(8), 1435–1441

    MathSciNet  Article  Google Scholar 

  22. Lyons, R. G. (2011). Understanding digital signal processing. (3rd ed.). Pearson Education.

    Google Scholar 

  23. Ma, T., Shen, C., & Wei, Y. (2019). Adjustable filter bank design for hearing aids system. In 2019 IEEE international symposium on circuits and systems (ISCAS) (pp. 1–5). IEEE.

  24. Mishra, A. K., Barik, R., & Paul, S. (2014). iACT: A software-hardware framework for understanding the scope of approximate computing. In Workshop on approximate computing across the system stack (WACAS) (p. 52).

  25. Mittal, S. (2016). A survey of techniques for approximate computing. ACM Computing Surveys (CSUR), 48(4), 62

    Google Scholar 

  26. Momeni, A., Han, J., Montuschi, P., & Lombardi, F. (2014). Design and analysis of approximate compressors for multiplication. IEEE Transactions on Computers, 64(4), 984–994

    MathSciNet  Article  Google Scholar 

  27. Nair, R. (2015). Big data needs approximate computing: Technical perspective. Communications of the ACM, 58(1), 104–104

    Article  Google Scholar 

  28. Narayanamoorthy, S., Moghaddam, H. A., Liu, Z., Park, T., & Kim, N. S. (2014). Energy-efficient approximate multiplication for digital signal processing and classification applications. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 23(6), 1180–1184

    Article  Google Scholar 

  29. Petra, N., De Caro, D., Garofalo, V., Napoli, E., & Strollo, A. G. (2009). Truncated binary multipliers with variable correction and minimum mean square error. IEEE Transactions on Circuits and Systems i: Regular Papers, 57(6), 1312–1325

    MathSciNet  Article  Google Scholar 

  30. Ramya, R., & Moorthi, S. (2019). Performance evaluation of wordlength reduction based area and power efficient approximate multiplier for mobile multimedia applications. Circuits, Systems, and Signal Processing, Springer, 38(12), 5699–5716

    Article  Google Scholar 

  31. Saramaki, T. (1987). Design of FIR filters as a tapped cascaded interconnection of identical subfilters. IEEE Transactions on Circuits and Systems, 34(9), 1011–1029

    Article  Google Scholar 

  32. Saramaki, T., & Mitra, S. K. (1993). Finite impulse response filter design, handbook for digital signal processing. Wiley-Interscience.

    Google Scholar 

  33. Sebastian, A., & James, T. G. (2015). Digital filter bank for hearing aid application using FRM technique. In 2015 IEEE international conference on signal processing, informatics, communication and energy systems (SPICES) (pp. 1–5). IEEE.

  34. Sengupta, D., & Saleh, R. (2007). Generalized power-delay metrics in deep submicron CMOS designs. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 26(1), 183–189

    Article  Google Scholar 

  35. Stine, J. E., & Duverne, O. M. (2003). Variations on truncated multiplication. In Proceedings Euromicro symposium on digital system design, 2003 (pp. 112–119). IEEE.

  36. Venkatachalam, S., & Ko, S. B. (2017). Design of power and area efficient approximate multipliers. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 25(5), 1782–1786

    Article  Google Scholar 

  37. Wei, Y., & Lian, Y. (2006). A 16-band nonuniform FIR digital filterbank for hearing aid. In Proceedings of the 2006 IEEE biomedical circuits and systems conference (pp. 186–189). IEEE.

  38. Wei, Y., Ma, T., Ho, B. K., & Lian, Y. (2018). The design of low-power 16-band nonuniform filter bank for hearing aids. IEEE Transactions on Biomedical Circuits and Systems, 13(1), 112–123

    Article  Google Scholar 

  39. Zendegani, R., Kamal, M., Bahadori, M., Afzali-Kusha, A., & Pedram, M. (2016). RoBA multiplier: A rounding-based approximate multiplier for high-speed yet energy-efficient digital signal processing. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 25(2), 393–401

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to S. Moorthi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ramya, R., Moorthi, S. Audiogram matching in hearing aid using approximate arithmetic. Multidim Syst Sign Process (2021).

Download citation


  • Approximate multiplier
  • Filter bank
  • Hearing aid
  • Audiogram