It is important to understand the rich structure of natural sounds in order to solve important
tasks, like automatic speech recognition, and to understand auditory processing
in the brain. This thesis takes a step in this direction by characterising the statistics of
simple natural sounds. We focus on the statistics because perception often appears to
depend on them, rather than on the raw waveform. For example the perception of auditory
textures, like running water, wind, fire and rain, depends on summary-statistics,
like the rate of falling rain droplets, rather than on the exact details of the physical
source.
In order to analyse the statistics of sounds accurately it is necessary to improve a
number of traditional signal processing methods, including those for amplitude demodulation,
time-frequency analysis, and sub-band demodulation. These estimation tasks
are ill-posed and therefore it is natural to treat them as Bayesian inference problems.
The new probabilistic versions of these methods have several advantages. For example,
they perform more accurately on natural signals and are more robust to noise,
they can also fill-in missing sections of data, and provide error-bars. Furthermore,
free-parameters can be learned from the signal. Using these new algorithms we demonstrate
that the energy, sparsity, modulation depth and modulation time-scale in each
sub-band of a signal are critical statistics, together with the dependencies between the
sub-band modulators. In order to validate this claim, a model containing co-modulated
coloured noise carriers is shown to be capable of generating a range of realistic sounding
auditory textures.
Finally, we explored the connection between the statistics of natural sounds and perception.
We demonstrate that inference in the model for auditory textures qualitatively
replicates the primitive grouping rules that listeners use to understand simple acoustic
scenes. This suggests that the auditory system is optimised for the statistics of natural
sounds