ACTA ACUSTICA UNITED WITH ACUSTICA Vol. 96 (2010) 383 – 396 DOI 10.3813/AAA.918287 Comparison of loudness models for time-varying sounds 3 Jan Rennies 1) ∗ , Jesko L. Verhey 1) , Hugo Fastl 2) 1) AG Neuroakustik, Institut für Physik, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany. jan.rennies@uni-oldenburg.de 2) AG Technische Akustik, Lehrstuhl für Mensch-Maschine-Kommunikation, Technische Universität München, D-80333 München, Germany Summary The loudness of a sound depends, among other parameters, on its temporal shape. Different loudness models were proposed to account for temporal aspects in loudness perception. To investigate different dynamic concepts for modeling loudness, predictions were made with the two current loudness models of Glasberg and Moore [J. Acoust. Soc. Am. 50, 331–341 (2002)] and Chalupper and Fastl [Acta Acustica united with Acustica 88, 378–386 (2002)] for a set of time-varying sounds. The predicted effects of duration, repetition rate, amplitude-modulation, temporal asymmetry, frequency modulation and the systematic variation of spectro-temporal structure on loud- ness were compared to data from the literature. Both models predicted the general trends of the data for single, repeated and asymmetric sound bursts and amplitude-modulated sounds. The model of Chalupper and Fastl seems to agree slightly better with loudness data for sounds with strong spectral variations over time, since it includes a dynamic stage which allows spectral loudness summation also for non-synchronous frequency components. PACS no. 43.66.Cb, 43.66.Ba, 43.66.Mk 1. Introduction Models for the prediction of loudness are valuable tools since they can at least partly replace time consuming sub- jective test. Accordingly, they are applied in a number of fields, e.g. in the assessment of noise emissions or the de- velopment and optimization of algorithms in hearing aids. Due to the practical relevance, different standards have been developed describing procedures to compute loud- ness (e.g. [2, 3]). However, all current loudness models are limited in their applicability to some extend. For ex- ample, the standardized procedures to calculate loudness mentioned above only provide valid loudness values for signals that are stationary. Since it is desirable to have a loudness model applicable to a wider range of sounds, it is first necessary to know the capabilities and limitations of current loudness models. This study compares the predic- tions of two elaborate current loudness models represent- ing different concepts for a set of time-varying sounds. In general, loudness models can be subdivided into models for stationary signals and those for time-varying Received 24 July 2009, accepted 30 November 2009. ∗ now at the Fraunhofer Institute for Digital Media Technology, Olden- burg, Germany 3 This study was partly done at the Technical University of Munich and partly at the University of Oldenburg. Part of the results were presented at the joint DAGA/NAG conference in Rotterdam in March 2009 [1]. sounds. Models for stationary signals disregard temporal properties of the sound and are based on the long-term spectrum of the signal. Apart from a weighting of the fre- quencies they also account for the effect of bandwidth on the overall loudness. If the bandwidth of a sound is varied while keeping the overall intensity fixed, loudness remains constant as long as the bandwidth is smaller than a criti- cal bandwidth, for larger bandwidths, loudness increases (e.g. [4, 5, 6, 7, 8, 9]). This effect called spectral loud- ness summation is believed to result from an analysis of the incoming sound by a bank of overlapping critical-band filters followed by a compressive nonlinearity in each fil- ter that transforms the intensity to specific loudness, and a final loudness summation across channels. The bandwidth of the auditory filters and the amount of compression af- fect spectral loudness summation, i.e. the narrower the au- ditory filters and the higher the compression, the larger the amount of spectral loudness summation (see [10]). This concept of spectral loudness summation has been imple- mented in a number of loudness models, which success- fully predict the loudness of stationary sounds as perceived by normal-hearing (e.g. [11, 12, 13, 14, 15, 16, 17]) and hearing-impaired listeners (e.g. [18, 19, 20, 21]). Most natural sounds, however, are non-stationary and have time-varying properties which also affect their loud- ness. For example, several studies found that loudness of sounds with the same intensity increases with duration (e.g. [22, 23, 24, 25, 26, 27, 28, 29, 30]. This effect is com- monly referred to as temporal integration of loudness. It is © S. Hirzel Verlag · EAA 383