Oscillations, Waves, and Interactions - GWDG

38 A. Kohlrausch and S. van de Par
listening booth, increased strongly throughout the 1980’s. This increased interest
was reflected even in a rebuilding of the central space in the “Halle” of the DPI, in
front of the “Reflexionsarmer Raum”, where the control panels for the loudspeaker
dome were dismantled and spaces for two listening booths were created. In parallel
with the acoustic spaces, also the computer infrastructure for controlling listening
experiments and generating signals with more complexity than contained in Gaussian
noise or sinusoids grew steadily in this period. In our view, this experimental
infrastructure together with a growing group of young scientists were essential for
the increasing level of sophistication of hearing research at the DPI. In the following,
we want to describe and analyze one of the factors, namely the creativity in using
signals with specific spectral and temporal properties in listening experiments and
model simulations. This creativity started at the DPI, but was spread to other places
like Eindhoven and Oldenburg, and more recently to Lyngby/Kopenhagen, and has
influenced many research paradigms in hearing research groups all over the world.
2 Harmonic complex tone stimuli
The first class of signals we will discuss are signals with a periodic waveform. Depending
on the way of construction of those signals, they are either considered in
the context of their temporal properties (e. g., when a regular series of clicks is generated
and the perceptual influence of a slight temporal deviation from regularity is
considered, see, e. g., Ref. [5]) or in the context of their spectral properties (consider,
e. g., the role of the vocal tract filter on the resulting vowel quality). Of course,
from a mathematical point of view, time-domain and spectral descriptions are fully
equivalent, if indeed not only the power spectrum, but the full complex spectrum,
including the phase, is considered. Historically, however, temporal and spectral views
were quite distinct, mainly under the influence of signal analysis systems that allowed
to represent the power spectrum, but not the phase spectrum. Also the paradigm of
critical bands and auditory filters, which for a long time were only defined in terms
of their overall bandwidth and their amplitude characteristics (see, e. g., Ref. [6]),
made it difficult to bring the temporal and spectral views closer together. Again,
the increasing use of computer programs to generate acoustic stimuli and to perform
time-domain modeling of perceptual processes emphasized the role of the phase
spectrum on the perceptual quality of periodic signals [7]. In the following, we will
focus on the description of one specific type of complex tones, those with so-called
Schroeder phases.
2.1 Schroeder-phase harmonic complex tones
2.1.1 Definition
The term Schroeder phase refers to a short paper by Schroeder from 1970 [8]. In
this paper, he addressed the problem how the peak-to-peak amplitude of a periodic
waveform with a given power spectrum can be minimized. He related this problem
to the observation that frequency-modulated stimuli have a low peak factor. The
proposed solution lies in a phase choice which gives the signal an FM-like property.