Abstract Numerous signal processing applications are emerging on mobile computing systems. These applications are subject to responsiveness constraints for user interactivity and, at the same time, must be optimized for energy efficiency. Many current embedded devices are composed of low-power multicore processors that offer a good trade-off between computational capacity and low power consumption. In this context, equalizers are widely used in multiple mobile-based applications such as “Music streaming” to adjust the levels of bass and treble in sound reproduction. In this study, we evaluate a graphic equalizer from audio, computational capacity, and energy efficiency perspectives, as well as the execution of multiple real-time equalizers running on an embedded quad-core processor of a mobile device. To this end, we experiment with the working frequencies as well as the parallelism that can be extracted from a quad-core ARM Cortex-A57. Results show that using high CPU frequencies and three or four cores, our parallel algorithm is able to equalize more than five channels per watt in real time with an audio buffer of 4096 samples, which implies a latency of 92.8 ms at the standard sample rate of 44.1 kHz.

Spatial audio-rendering techniques using head-related transfer functions (HRTFs) are currently used in many different contexts such as immersive teleconferencing systems, gaming, or 3-D audio reproduction. Since all these applications usually involve real-time constraints, efficient processing structures for HRTF modeling and interpolation are necessary for providing real-time binaural audio solutions. This letter presents a parametric parallel model that allows us to perform HRTF filtering and interpolation efficiently from an input HRTF dataset. The resulting model, which is an adaptation from a recently proposed modeling technique, not only reduces the size of HRTF datasets significantly, but also allows for simplified interpolation and real-time computation over parallel processors. In order to discuss the suitability of this new model, an implementation over a graphic processing unit is presented.

In the audio signal processing field, multiple IIR filters are required in many applications. As an example, equalizing a Wave Field Synthesis system requires massive filter processing in real time. Graphics Processing Units (GPUs) are well known for their potential in highly parallel data processing. Up to now, the use of the GPUs for implementing IIR filters has not been clearly tackled in audio processing because of its feedback loop that prevents its total parallelization. However, using the Parallel form of IIR filters, this feedback is reduced, since every single sample is computed in a parallel way. This paper analyzes the performance of multiple IIR filters using GPUs and compares it with a powerful multi-core computer. The proposed GPU implementation can run up to 1256 concurrent IIR filters of order 256th in real time, which means 321,536 total filter order, with a latency time of 0.72 ms (sampling frequency of 44.1 kHz). This demonstrates that GPUs are well suited for computing massive IIR filtering.

This paper proposes a high-precision graphic equalizer 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 structure. 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.

Recently, the fixed-pole design of second-order parallel filters has been introduced to accomplish arbitrary (e.g., logarithmic) frequency resolution for transfer function modeling and equalization. The frequency resolution is set by the pole frequencies, and the resulting filter response corresponds to the smoothed (moving-average filtered) version of the target frequency response. This letter presents the frequency-domain version of the design algorithm for complex and real filter coefficients. The proposed frequency-domain design, besides its computational benefits, allows the use of frequency weighting. In addition, a magnitude-only variation of the algorithm is proposed. Examples of loudspeaker-room modeling and equalization are presented.

The use of second-order parallel filters with pre-defined pole locations has been recently proposed for equalization and transfer function modeling. This letter presents an improved method for obtaining the pole positions of the parallel filter. The steps of the new method are the following: first, the target frequency response is smoothed to the required resolution. Then, multiple warped IIR filters with different warping parameters are designed to the smoothed target divided into frequency bands. Finally, the united pole set of the warped IIR designs is used for parallel filter design. The method leads to increased accuracy compared to earlier pole positioning techniques, and can also be used for Kautz filter designs. Examples of loudspeaker-room response modeling and equalization are presented.

This paper presents a real-time piano synthesizer where both the transverse and longitudinal motion of the string is modeled by modal synthesis, resulting in a coherent and highly parallel model structure. The paper applies recent developments in piano modeling and focuses on the issues related to practical implementation (e.g., numerical stability, aliasing, and efficiency). A strong emphasis is given to modeling nonlinear string vibrations, and a new variation of earlier synthesis techniques is proposed which is particularly well suited for modal synthesis. For soundboard modeling, the possibilities of using fast Fourier transform-based fast convolution and parallel second-order filters are discussed. Additionally, the paper describes the details of the software implementation and discusses the computational complexity of each model block. The piano model runs on current computer hardware with full polyphony in real time.

In audio, equalizer design should take into account the frequency resolution of the auditory system. In this paper, this is accomplished by the fixed-pole design of parallel second-order filters. The design process has two steps: first, the poles of the filter are set according to the desired frequency resolution. Then, the feedforward coefficients of the second-order filters are determined by a linear least squares solution. The proposed parallel filter achieves effectively the same equalization results as the Kautz filter, but it requires 33% fewer multiplications and additions.

A robust loss filter design method is presented for digital waveguide string models, which can be used with high filter orders. The method aims at minimizing the decay time error in partials of the synthetic tone. This is achieved by a new weighting function based on the first-order Taylor series approximation of the decay time errors. Smoothing of decay time data and requiring the design to be minimum-phase are also proposed to facilitate the stability of the design. The new method is applicable to analysis-based sound synthesis of piano and guitar tones, for example.