# Designing Audio Equalization Filters by Deep Neural Networks
## 1 Introduction  
Listening environments are characterized by reflections and reverberations that can adversely affect listening [1] and attention [2], adding unwanted artifacts to the sound produced by an acoustic source. For this reason, audio equalization is needed in order to improve sound quality reproduction. Of particular interest is the car scenario, where people daily listen to music, radio programs or take hands-free phone calls. The audio quality in such an environment is very important, but is adversely affected by several factors, including the loudspeakers quality and the reflective materials inside the cabin. The impulse response at the listening position is characterized by the sum of multiple signals: those coming from the loudspeakers and their reflections. Furthermore, the loudspeakers impose their frequency response on the signal. The frequency response is thus colored and usually results in deep notches and peaks, that reduce the audio quality. These issues are generally addressed by the design of linear filters [3] that are applied to the signal before being transduced by the loudspeakers. The filters are designed to improve the audio quality at specific listening positions by inverting the car impulse response. However, the task is challenging, as the existence of the inverse may not be guaranteed, and the complexity increases with the number of sources and microphones. A plethora of design techniques have been proposed in the past for room equalization [1], and some have been proposed, more specifically, for the car scenario. These are, generally, based on linear optimization and inversion algorithms. Considering the complexity of this task, however, novel design techniques may be applied in this context, relying on nonlinear methods such as evolutionary algorithms, machine learning and neural networks. Since digital communication systems are subject to the multipath problem, that is, the sum of multiple reflections in a linear channel with multiple sources and receivers, it is worth investigating the literature for equalization techniques applied to this application field. Indeed, several novel techniques have been proposed for the design of equalizing filters for digital communications, relying on nonlinear methods. In Reference [4], the authors use Particle Swarm Optimization (PSO) to equalize the impulse response of an optical fiber communication. This is shown to provide better results than Least Mean Square (LMS) and Recursive Least Square (RLS) techniques. Another interesting PSO approach is reported in Reference [5], where the PSO particles are used to obtain optimal poles and zeros of an IIR filter. In Reference [6] Genetic Algorithms (GA) are exploited for Adaptive Channel Equalization, in order to reduce the Inter Symbol Interference (ISI) present in the trasmission channel. Although inspiring, these algorithms cannot be employed in the audio equalization scenario, as the two tasks differ in several aspects. While in communication systems equalizers are implemented at the receiving end, in the audio case they can only be implemented at the sound source. This can represent an issue, as the equalizing filters must provide satisfying results at several listening positions, while with telecommunication devices, each one can adapt its equalizing filter depending on the incoming signal. In communication systems the main goal is reducing symbol error rate, thus, allowing a robust classification of the symbols constellation, while in the audio field the goal is to achieve near-perfect audio quality taking psychoacoustic factors into consideration. Finally, the communication scenario may or may not consider time-varying environmental conditions (e.g., mobile receiving stations), while in the audio field time-invariance is often assumed, thus, room impulse responses are measured and treated statically.