Abstract
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.
Highlights
The design of digital graphic equalizers (GEQ) has advanced considerably during the past five years [1,2,3]
The proposed design allows the parametric EQ used as band filters in the GEQ to have a controllable gain at the Nyquist limit, in contrast to the earlier designs that forced the Nyquist gain to one (i.e., 0 dB) [3]. This paper extends both the weighted least-squares (WLS) GEQ design method and the neurally-controlled EQ method to operate in Bark bands, which are a more accurate approximation of the human auditory resolution than the third-octave bands [23]
This paper introduced an improved cascade design for auditory graphic equalizers having either a third-octave or a Bark band division
Summary
The design of digital graphic equalizers (GEQ) has advanced considerably during the past five years [1,2,3]. GEQs [8,9,10,11,12,13] For both octave and third-octave bands, designing either a cascade [3,6] or a parallel GEQ [10,11,13] having a maximum error of 1 dB, often considered sufficient for Hi-Fi audio, is possible. This work considers the design of a cascade GEQ having an auditory frequency resolution that is similar to human hearing, such as the third-octave and the Bark frequency divisions. Auditory filters such as Bark filters are implemented using a filter bank that decomposes the input signal into different frequency bands by using bandpass filters [14,15,16].
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