# Designing Audio Equalization Filters by Deep Neural Networks
## 1 Introduction
A first attempt at the use of deep learning for audio equalization is found in Reference [7], where the authors use a Time Delay Neural Network (TDNN) to solve the problem of equalization, using the input sequence, delayed by a time unit, as input and the signal recorded by the microphone as output the error between the input signal and the output of the network is used for the back-propagation algorithm. The forward approach is also employed using a delayed copy of the input signal as input and the difference between the output given from the loudspeaker and the network as error. In References [8; 9], the authors describe a system that maps the gain of each frequency band with the user's preferred equalizer settings as training data. A similar approach is undertaken in Reference [10], where k-Nearest Neighbour (KNN) is used to implement a timbre equalizer based on user preference in terms of brightness, darkness and smoothness. Specifically, sound professionals and music students were asked to manually equalize 41 audio segments. Equalization for music production were performed in Reference [11], where a Dilated Residual Network (DRN) was used to automate the resonance equalization in music, predicting the optimal attenuation factor, while an end-to-end equalization was used in Reference [12], substituting filter banks with Convolutional Neural Network (CNN) and without prior knowledge of filter parameters, like gains, cut-off frequency and quality factor. Recent works addressing the design of IIR filters using PSO can be found in References [13; 14; 15]. In particular, [PERSON] et al. [15] use PSO with fractional derivative constraints to design a quasi-linear phase IIR filter for Audio Crossover Systems. The algorithm gives the parameters of the desired filter (like cut-off frequency) with a flat magnitude response and a linear phase. In Reference [16], the authors use Gravitational Search Algorithm (GSA) to model an IIR filter and a nonlinear rational filter, then they compare the technique with PSO and GA. In this case, the algorithms provide filter coefficients as outputs. Another approach is used in Reference [17], where the authors achieved an IIR filter using the Artificial Immune Algorithm and compared the results with GA, the Touring Ant Colony Optimization (TACO) and Tabu Search (TS). Neural networks have been also proposed for the filter design task. In Reference [18] a neural network is devised to design an IIR filter with the error calculated as the difference in magnitude response between the desired and the generated filter. [PERSON] et al. [19] provide a performance comparison of some neural network architectures to design a low pass Finite Impulse Response(FIR)filter, including Radial Basis Function (RBF), General Regression Neural Networks (GRNN), Radial Basis Exact (RBE), Back-Propagation Neural Network (BPNN) and the Multilayer Perceptron (MLP). [PERSON] et al. [20] proposes a two step optimization Frequency-Response Masking (FRM) technique based on the design of a FRM filter optimizing the subfilters, further optimized by decomposing it into several linear neural networks. In previous work from the same authors [21], evolutionary algorithms were employed for binaural audio equalization in the car cabin. PSO and GSA were tested, leading to an improvement with respect to baseline techniques. In this work we introduce a different approach, based on deep neural networks, with the aim of improving previous results and broadening the scope to multipoint equalization. To the best of our knowledge, no deep learning technique has been proposed in the literature to obtain filter coefficients for multipoint audio equalization. In this work we conduct the offline design of the filters coefficients exploiting deep neural networks trained according to a set of frequency-domain constraints. Three architectures are proposed and several experiments are conducted in two car cabins characterized by multiple impulse responses, comparing the results of the proposed method to the state of the art methods.