Pole Optimization of IIR Filters Using Backpropagation

Abstract

Audio signal processing is a field where specialized techniques are used to account for the characteristics of hearing. In filter design the resulting transfer function need to follow the specification on an approximately logarithmic frequency scale, which can be done via methods such as frequency warping or fixed-pole parallel filters. Although these IIR filter design techniques are proven in practice, they do not produce optimal pole sets for the given specification. In this paper we present the first experiments of using a gradient-based pole optimization framework implemented in TensorFlow by realizing the IIR filter as a recurrent neural network (RNN). The method can improve the pole set of a filter compared to the initial pole set, resulting in a smaller approximation error. The proposed method is demonstrated using four example filter specifications.