posted 13 November 2002 02:15            

In my work with image processing, pattern recognition, and compression, I have been making use of the Gabor Wavelets -- named for the same physicist who gave birth to granular synthesis...

A Gabor wavelet is really nothing more than a Gaussian windowed bandpass filter. But it exhibits very desirable properties with respect to Affine transformations of images -- scaling, translation, and rotation. It also satisfies an optimal uncertainty relationship simultaneously in the spatial and spatial frequency domain.

...so this leads me to wonder about its use in the one-dimensional time domain of signal processing. Instead of using STFFT's to analyze frequency and phase variations in a sound morphing application, might not the use of a one-dimensional Gabor Wavelet be even better suited to this task? Here we have to contend only with scaling and translation. There is no equivalent to rotation in only one dimension.

Right now the sound analysis engine asks us to choose between various windowing periods for optimizing either of pitch recognition or temporal location accuracy of events. With a set of Gabor Wavelets, these two would be simultaneously and independently optimized at each analysis frequency. There would be no need to make a choice in this analysis, because at each frequency the width of the Gaussian envelope would be optimally chosen for that frequency.

Any thoughts on this?

- DM

[PS... Yes, the full out Gabor Wavelet analysis would be very computationally expensive. But there are a number of fast and accurate approximations in use for image processing. I'm not sure how badly their artifacts would sound in the time domain. I just started thinking about this...]

posted 21 January 2003 10:21            

The goal of the author's work is to stretch a sample into an infinitely sustained sound using granular synthesis. The basic technique described in the paper is:

1. Segment a sample into "natural grains"

2. Using wavelet analysis, measure the similarity of the grains to each other

3. Synthesize an "infinite" sound by playing a stream of these grains, randomly selecting the next grain to be played, but choosing similar grains more often than dissimilar grains

posted 21 January 2003 17:22            

Thanks for explaining the technique to us common folk. I guess that the thesis/application/Java source code could not be translated into wavelet analysis prototype within Kyma?