Direct design of biquad filter cascades with deep learning by sampling random polynomials (2110.03691v2)

Abstract: Designing infinite impulse response filters to match an arbitrary magnitude response requires specialized techniques. Methods like modified Yule-Walker are relatively efficient, but may not be sufficiently accurate in matching high order responses. On the other hand, iterative optimization techniques often enable superior performance, but come at the cost of longer run-times and are sensitive to initial conditions, requiring manual tuning. In this work, we address some of these limitations by learning a direct mapping from the target magnitude response to the filter coefficient space with a neural network trained on millions of random filters. We demonstrate our approach enables both fast and accurate estimation of filter coefficients given a desired response. We investigate training with different families of random filters, and find training with a variety of filter families enables better generalization when estimating real-world filters, using head-related transfer functions and guitar cabinets as case studies. We compare our method against existing methods including modified Yule-Walker and gradient descent and show our approach is, on average, both faster and more accurate.

• The paper introduces IIRNet, a neural network that directly maps target magnitude responses to biquad filter coefficients.
• The paper leverages millions of randomly sampled polynomials for training, achieving lower mean squared errors and faster designs than traditional methods.
• The paper validates the approach on real-world datasets, demonstrating enhanced accuracy in audio processing and control systems.

Direct Design of Biquad Filter Cascades with Deep Learning by Sampling Random Polynomials

This paper presents a novel approach to designing Infinite Impulse Response (IIR) filters by leveraging deep learning to predict filter coefficients directly. The methodology involves using a neural network, IIRNet, which learns to map a target magnitude response to the coefficients of a biquad filter cascade. The trained model, based on millions of random filters, provides a more accurate and efficient design compared to classical techniques.

Technical Overview

The primary contribution of this work lies in its innovative utilization of a neural network to bypass the limitations of traditional IIR filter design methods such as modified Yule-Walker and iterative gradient-based optimization. Classical methods often compromise between speed and accuracy, with the former sometimes lacking precision and the latter being computationally expensive and sensitive to initial conditions.

IIRNet is trained using a diverse set of random filters generated from various families of random polynomials, including normal coefficients, characteristic polynomials of random matrices, and parametric EQs, among others. This diversity allows the model to generalize better when estimating filters in real-world scenarios. The model architecture itself is composed of linear layers enhanced with techniques like layer normalization and nonlinear activation functions for robust training.

Strong Numerical Results

The paper provides quantitative evidence of IIRNet's superior performance. Across a variety of datasets, including artificial random filters and real-world data like head-related transfer functions (HRTFs) and guitar cabinet impulse responses, IIRNet demonstrates enhanced accuracy and reduced run-time when compared to both modified Yule-Walker and gradient descent approaches. Specifically, IIRNet outperforms modified Yule-Walker across random filter families and the guitar cabinet dataset despite the latter's superior performance with HRTFs, likely due to their limited dynamic range.

Additionally, models trained with all random filter families consistently deliver the lowest mean squared errors, highlighting the efficacy of incorporating diverse training data to improve generalization.

Implications and Future Directions

The implications of this research are noteworthy both in practical and theoretical contexts. Practically, the ability to rapidly and accurately design IIR filters can significantly enhance applications in audio signal processing and control systems, among others. Theoretically, the paper opens avenues for further exploration into the integration of deep learning within classical signal processing domains.

Future research could focus on addressing the limitations noted by the authors, such as extending IIRNet to estimate variable filter orders and considering both magnitude and phase responses in designs. Another intriguing direction would be to refine IIRNet estimations through hybrid approaches combining initial design by IIRNet followed by targeted iterative optimization for specific constraints or applications.

In summary, this work exemplifies a significant advancement in IIR filter design, with its empirical results validating the potential of deep learning models like IIRNet to transcend traditional approaches, offering a compelling blend of efficiency and accuracy in practical applications.