Gradient descent based adaptive IIR filtering with direct and lattice form filter structures; applied to estimation of a headphone compensation filter and binaural head related transfer functions

Abstract

In acoustic Digital Signal Processing (DSP), Finite Impulse Response (FIR) filters are commonly used due to their stability and ease of design. However, Infinite Impulse Response (IIR) filters offer better frequency resolution at lower filter orders, making them ideal for hardware-constrained applications like portable AR/VR headsets. With advances in computational methods, optimising IIR filters has become straightforward, making it important to compare their performance against traditional FIR filters. This thesis investigates adaptive IIR filtering algorithms using Gradient Descent (GD) methods, applied to both direct form and lattice form filter structures. Lattice form filter structures provide the benefit of an in-built stability test which can guarantee that the produced IIR filter remains stable at each step. This is essential for reliable IIR filter design and allows for further modifications to the optimisation routine. For the studies, the Modified GD direct form and the Simplified Partial Gradient Descent (SPGD) lattice form algorithms were used to model a headphone compensation filter and binaural Head-Related Transfer Function (HRTF), comparing the resulting IIR filters to equivalent FIR filters. Parameter studies on step-size coefficient and filter order were conducted to assess accuracy in both frequency and time domain. The study found that both IIR filter forms reduced order length to 20% of the HRTF filter order and 40% of the compensation filter order, both within a 1 dB accuracy threshold in the magnitude response. This results in reduction in numerical operations of 60% for the HRTF filter and 20% for the headphone compensation filter. This work demonstrates the that significant order reduction is possible using lattice form, gradient decent based adaptive filters. The exact reduction depends on the target filter and requires similar simulations and analysis to those used here.