THE ERBLET TRANSFORM: AN AUDITORY-BASED TIME-FREQUENCY REPRESENTATION WITH PERFECT RECONSTRUCTION

ABSTRACT This paper describes a method for obtaining a perceptually motivated and perfectly invertible time-frequency representation of a sound signal. Based on frame theory and the recent non-stationary Gabor transform, a linear representation with resolution evolving across frequency is formulated and implemented as a non-uniform filterbank. To match the human auditory time-frequency resolution, the transform uses Gaussian windows equidistantly spaced on the psychoacoustic "ERB" frequency scale. Additionally, the transform features adaptable resolution and redundancy. Simulations showed that perfect reconstruction can be achieved using fast iterative methods and preconditioning even using one filter per ERB and a very low redundancy (1.08). Comparison with a linear gammatone filterbank showed that the ERBlet approximates well the auditory time-frequency resolution

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Verbenone—the universal bark beetle repellent? Its origin, effects, and ecological roles

Bark beetles (Curculionidae: Scolytinae) spend most of their life in tissues of host plants, with several species representing economically relevant pests. Their behaviour is largely guided by complex olfactory cues. The compound verbenone was discovered early in the history of bark beetle pheromone research and is now sometimes referred to as a ‘universal bark beetle repellent’. However, some studies aiming to protect trees with verbenone have failed. In fact, most research effort has gone into applied studies, leaving many questions regarding the ecological functions of verbenone for various species unanswered. Here, we review and analyse the scientific literature from more than 50 years. Behavioural responses to verbenone are common among pest bark beetles (< 1% of scolytine species studied so far). Indeed, attraction is inhibited in 38 species from 16 genera, while some secondary species are unaffected or even attracted to verbenone. It is not clear whether the beetles can control the biosynthesis of verbenone; its release may not be an active signal by the beetles, but a passive cue resulting from microorganisms during host colonisation. In this context, we advocate to recognise a bark beetle and its microbiome as an entity (‘holobiont’), to better understand temporal release patterns and deduce the specific function of verbenone for a given species. Surprisingly, natural enemies are not commonly attracted by verbenone, but more taxa need to be studied. A better understanding of the ecological functions of verbenone will help to make verbenone-based tools more effective and improve integrated pest management strategies