Graphic Equalizer Design with Symmetric Biquad Filters

Abstract

A novel graphic equalizer design comprised of a single secondorder section per band is proposed, where the band filters have a symmetric shape about their center frequency in the entire audio range. The asymmetry of the band filters at high frequencies close to the Nyquist limit has been one source of inaccuracy in previous designs. The interaction between the different band filters is accounted for using the weighted least-squares design, which employs an interaction matrix. In contrast to prior works, the interaction matrix is designed with a different prototype gain for each band filter, helping to keep the maximum approximation error below 1 dB at the center frequencies and between them when the neighboring command gains are the same. An iteration step can further diminish the approximation error. Comparisons of the proposed design with previous methods show that it is the most accurate graphic equalizer design to date.

Third-Octave and Bark Graphic-Equalizer Design with Symmetric Band Filters

“…Furthermore, similar design methods are used to provide a design for a novel Bark band GEQ (SGEB). In the proposed GEQ designs, the band filters have a symmetric magnitude response on the logarithmic frequency scale, as suggested in [22]. This symmetry affects primarily the shape of the band filter magnitude response at high frequencies, which allows the band filters to have a specific gain at the Nyquist limit.…”

“…The design formulas for the symmetric band filters were obtained by modifying those suggested by Orfanidis [31] so that the filter gain at DC (i.e., 0 Hz) was unity and the gain G Nq,m at the Nyquist limit was adjustable instead of prescribed based on the analog filter counterpart [22,31]. The transfer function of the resulting second-order band filter, implemented with the structure in Figure 2, is:…”

“…The Nyquist gain for each band filter was calculated with the help of a sufficiently highly oversampled parametric EQ filter emulating the shape of an analog filter, as proposed in [22]. The sample rate was set to 10 MHz, and the filter gain was evaluated at 22.05 kHz, which was the Nyquist limit f s /2 at the sample rate of 44.1 kHz.…”

“…2020, 10, 1222 2 of 22 using a neural network, which handled the optimization calculation [19]. The second paper extended the neurally-controlled equalizer (EQ) method to the widely used third-octave GEQ design [20], where the 31 EQ bands also loosely approximated the bandwidths of human auditory filters [21].Compared to our previous conference paper [20], this article presents an improved design method using second-order band filters with a symmetric shape on the logarithmic frequency scale, which was recently proposed for an octave GEQ [22]. 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].…”

“…Compared to our previous conference paper [20], this article presents an improved design method using second-order band filters with a symmetric shape on the logarithmic frequency scale, which was recently proposed for an octave GEQ [22]. 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].…”