AES Fall Convention 2022

Algorithmic reverberation aims to synthesize natural-sounding reverberation. Many signal processing architectures have been established to provide parametric control to generate custom and good-sounding reverberation.

A recorded room impulse response offers an exhaustive representation of the sound characteristics of a reverberant space at a given point. Convolution between the room impulse response and an audio signal renders a reverberated signal with the characteristics of the room. However, impulse response convolution provides only very limited parametric control over the reverberation characteristics. Also, the number of computing operations required to convolve an impulse response can be very large, making it less suitable for embedded systems. To counter those limitations, one solution is to use algorithmic reverberation to simulate the general effects of a reverberant environment. Ideally, such an approach should match the effects of a room impulse response.

This paper presents an approach to match a target impulse response using feedback delay network (FDN). FDN is a commonly used algorithmic reverberation design. Our method provides a fully parametric reverberation, with precise control over energy decay based on a target impulse response We begin by providing a review of existing approaches. Most of the approaches use genetic algorithms. More recently, deep learning approaches have been applied, but these are challenging since FDN are hardly differentiable which makes gradient backpropagation difficult.

We then describe our methodology, providing the dataset and procedure developed to generate matched impulse responses. We use an analysis-synthesis approach coupled with genetic algorithms to find the vector of parameters of the FDN that provides the best match between the two impulse responses.

First, we analyze an impulse response and get its characteristics such as reverberation time, energy decay curve, clarity, and echo density. Next, we convert those measurements into coefficient values for the FDN reverberation. Delay lengths and input and output gains of the FDN cannot be directly calculated from the impulse response analysis. We run a genetic algorithm to find the best values for those coefficients.

We established a cost function to emphasize the psychoacoustical differences between impulse responses by giving more weight to low frequencies of the error spectrum and error in the early reflections.

We are currently conducting a subjective test to assess if participants perceive differences between our synthesized impulse responses and the targets using the MUSHRA test method. We compare our best full impulse response, our best hybrid impulse response (which is generated with the direct convolution of the early reflections and then goes into an FDN for late reverberation synthesis), the target (as control), and a low-pass filtered version of the target impulse response as an anchor.

Differences are perceptible if we try to match the entire impulse response only with an FDN, Hybrid impulse responses give better results and lower error overall.

Our methodology gives good results for late impulse response synthesis, but most of the error resides in the early reflections and has a significant impact on the perceived difference by a listener. We discuss how to improve our reverberation design to match early reflections in future works. We also discuss how to develop a method to match any room impulse response with any algorithmic reverberation design using machine learning.