1894 IEEE/ACM TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 22, NO. 12, DECEMBER 2014 High-Precision Parallel Graphic Equalizer Jussi Rämö, Vesa Välimäki, Senior Member, IEEE, and Balázs Bank, Member, IEEE Abstract—This paper proposes a high-precision graphic equal- izer based on second-order parallel filters. Previous graphic equalizers suffer from interaction between adjacent band filters, especially at high gain values, which can lead to substantial errors in the magnitude response. The fixed-pole design of the proposed parallel graphic equalizer avoids this problem, since the parallel second-order filters are optimized jointly. When the number of pole frequencies is twice the number of command points of the graphic equalizer, the proposed non-iterative design matches the target curve with high precision. In the three example cases presented in this paper, the proposed parallel equalizer clearly outperforms other non-iterative graphic equalizer designs, and its maximum global error is as low as 0.00–0.75 dB when compared to the target curve. While the proposed design has superior accuracy, the number of operations in the filter structure is increased only by 23% when compared to the second-order Regalia–Mitra struc- ture. The parallel structure also enables the utilization of parallel computing hardware, which can nowadays easily outperform the traditional serial processing. The proposed graphic equalizer can be widely used in audio signal processing applications. Index Terms—Acoustic signal processing, audio systems, digital signal processing, equalizers, infinite impulse response (IIR) filters. I. INTRODUCTION E QUALIZERS are a common part of modern audio systems. They were originally used to flatten, i.e., to equalize, telephone and audio systems. With telephones using fixed equalizers to enhance the intelligibility of the speech signal was adequate, but the need for an adjustable equalizer emerged in the 1930s when a recorded soundtrack was included in motion pictures [1]. Nowadays the goal of equalizing is not necessarily to flatten out the response of an audio system but rather to correct or enhance the performance of the system [2]. This includes, e.g., the correction of a loudspeaker response [3]–[5] and the loudspeaker-room interaction [6]–[10], equalization of active as well as passive headphones to assure natural music listening [11]–[14] and hear-through [15]–[17] experiences when using headphones, and enhancement of recorded music [18], [19]. A basic common equalizer is called a tone control. Tone con- trols can be found in many commercial audio products, and, at Manuscript received December 19, 2013; revised May 09, 2014; accepted August 27, 2014. Date of publication September 04, 2014; date of current ver- sion September 16, 2014. The work of B. Bank was supported by the Bolyai Scholarship of the Hungarian Academy of Sciences. The associate editor co- ordinating the review of this manuscript and approving it for publication was Prof. Søren Holdt Jensen. J. Rämö and V. Välimäki are with the Department of Signal Processing and Acoustics, School of Electrical Engineering, Aalto University, 02150 Espoo, Finland (e-mail: jussi.ramo@aalto.fi; vesa.valimaki@aalto.fi). B. Bank is with the Department of Measurement and Information Systems, Budapest University of Technology and Economics, 1117 Budapest, Hungary (e-mail: bank@mit.bme.hu). Digital Object Identifier 10.1109/TASLP.2014.2354241 its simplest, it allows the user to adjust the level of bass and treble with two shelving filters [20]. When more than two filters are combined in a tone control system, which is common, e.g., in musical instrument amplifiers [21], [22], the user’s possibil- ities to modify the sound are increased. There are two main types of equalizers. When the user can control the gain, center frequency, and bandwidth of the equal- izer filters separately, the equalizer is called a parametric equal- izer [23]–[27]. A parametric equalizer is flexible and the user has good control of it, but it is quite cumbersome to use requiring an expert user, such as an audio engineer or a music producer, and it usually has a limited number of filters that the user can adjust. A graphic equalizer, on the other hand, is much simpler to use than a parametric equalizer, since the only user-controllable pa- rameters are the gains. The center frequencies and bandwidths of the equalizer filters, or band filters, are fixed, and the com- mand gains are usually adjusted using sliders [28]–[30]. The sliders then plot the approximate magnitude frequency response of the equalizer, hence the name ‘graphic equalizer’. Typically, a graphic equalizer has more bands, i.e., equalizer filters, than a parametric equalizer. Although the flexibility of a graphic equal- izer is not as good as that of a parametric equalizer, it is often a preferred choice in sound enhancement. A graphic equalizer can be implemented using a cascade [23], [29], [31] or a parallel [28], [30], [32] filter structure. In a cas- cade implementation, each band filter adjusts its magnitude re- sponse around its center frequency according to the command gain, but the magnitude response of the band filter remains close to unity, i.e., 0 dB, elsewhere. In a parallel implementation, each band filter produces a resonance at its center frequency and has a low gain at other center frequencies. Both types of equalizers suffer from interaction between adjacent band filters, which can cause substantial errors in the magnitude response [31]–[33]. This paper presents a novel idea to utilize an optimized parallel filter as a graphic equalizer. The fixed-pole design of second-order parallel filters was first presented in [34] as a means of providing efficient filtering with logarithmic fre- quency resolution, which is often required in audio applications [35], [36]. The use of parallel filters in our context is motivated by the fact that it provides better efficiency compared to alter- native methods, including warped [37] and Kautz filters [38], as demonstrated in [39], [40]. An additional benefit of the parallel structure is the possi- bility to implement the equalization filters using a graphic pro- cessing unit (GPU) instead of a central processing unit (CPU) [41]. GPUs have a large number of parallel computing cores, and they have been recently used to perform audio signal pro- cessing as well, since they can outperform a CPU in many par- allelizable tasks [42]. 2329-9290 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.