Time Structure Analysis of Fan Sounds
In general the sound of air delivering fans or fan systems is described by listeners utilizing descriptors like loudness, pitch, timbre, etc. but also by time-related adjectives such as rattling, fluttering or blowing. The time variance of a sound over time can lead to the perception of unpleasantness or annoyance, which in turn classifies a product as of minor sound quality. In this paper we investigate whether the concept of the psychoacoustic metric "roughness" is useful to evaluate time-related sound properties of fan sound with respect to its sensed quality. In a psychoacoustic analysis different algorithms for determining the metric "roughness" are in use, e.g. by Sottek, Daniel and Weber or Oetjen et al. They proved to be useful mainly for simple sinusoidal sounds. Modulation frequencies up to about 20 Hz are perceived as rhythm. The variation can be in frequency, e.g. used for a siren, or in amplitude, e.g. the audible beat when tuning a guitar. With increasing frequency the perception changes to impure or rough which is mathematically described by roughness. Typically, for complex sounds of fans the available algorithms are insufficient to yield values of roughness which reflect the results of jury tests.
In a first analysis, it was found that the sound of fan and fan systems is not modulated just by one modulation frequency. A huge amount of different solitary frequencies or narrow bands can be found, which also may vary randomly over time. For that, the statistical parameter "Shannon entropy", which is a metric for the randomness of distribution of events, was used. In a second step the perception of fan sounds with various different time structures is evaluated by jury tests. Finally, the difference between jury rating and the value of Sottek roughness is attributed to the different values of the Shannon entropy associated with each sound. In analogy to a study of Oetjen et al. we suggest and assess an improved concept of roughness for fan sound by taking into account the Shannon entropy, i.e. a parameter for the randomness of the modulation spectrum in time.