Third-octave and Bark graphic-equalizer design with symmetric band filters

Jussi Rämö*, Juho Liski, Vesa Välimäki

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)
80 Downloads (Pure)


This work proposes graphic equalizer designs with third-octave and Bark frequency divisions using symmetric band filters with a prescribed Nyquist gain to reduce approximation errors. Both designs utilize an iterative weighted least-squares method to optimize the filter gains, accounting for the interaction between the different band filters, to ensure excellent accuracy. A third-octave graphic equalizer with a maximum magnitude-response error of 0.81 dB is obtained, which outperforms the previous state-of-the-art design. The corresponding error for the Bark equalizer, which is the first of its kind, is 1.26 dB. This paper also applies a recently proposed neural gain control in which the filter gains are predicted with a multilayer perceptron having two hidden layers. After the training, the resulting network quickly and accurately calculates the filter gains for third-order and Bark graphic equalizers with maximum errors of 0.86 dB and 1.32 dB, respectively, which are not much more than those of the corresponding weighted least-squares designs. Computing the filter gains is about 100 times faster with the neural network than with the original optimization method. The proposed designs are easy to apply and may thus lead to widespread use of accurate auditory graphic equalizers.

Original languageEnglish
Article number1222
Number of pages22
JournalApplied Sciences (Switzerland)
Issue number4
Publication statusPublished - 1 Feb 2020
MoE publication typeA1 Journal article-refereed


  • Audio signal processing
  • Digital filters
  • Equalizers
  • Hearing
  • IIR filters
  • Supervised learning


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