The Discrete Wavelet Transform (DWT) is a mathematical technique used mostly for signal and image analysis. Our research goal was to find out if there would be any use for it as applied to digital audio synthesis: the algorithmic generation of sound using only computers. Our interests are motivated primarily by electronic music. Producers in this genre of music are interested in finding interesting ways to make new sounds. I know, because I am one of them. According to subject matter experts, we aren’t the first group to try using the DWT for music. Unfortunately, there is virtually no documentation of prior attempts or findings, apparently because no one found any use for it. Let us introduce our efforts. A research poster and demonstration of the sounds are available for download above. This research was carried out with funding from California Institute for Telecommunications and Information Technology (Calit2).

It is fair to ask, “Why wavelets?” Wavelets are small pulses that are carefully constructed with very specific mathematical properties. We can decompose a signal into combinations of these very delicate pulses, then reconstruct the exact original signal from them. What we’ve done is akin to smashing a Rolex and using the little parts that come flying out as confetti. What appealed to us about this method was the time-frequency representation of signals. Another factor is that there is much infrastructure already in place to implement the DWT, so less work. With that said, we found little use for using wavelets, specifically, for sound synthesis. So our focus has changed somewhat since the original project was proposed.

We can abandon the constraint that the wavelets actually be of any precise mathematical form. We will just call them pulses from this point forward. Our new model will take an input waveform (say, the same that we started with in the DWT experiment) and expand it in time for each higher octave of the filter bank. These pulses will be fed into the reconstruction filters as before. Now we can experiment with different forms for the filter coefficients. What constraints would we put on such a filter? We want linear-phase so that we can line up the different channels at the end of the filter bank. We also want to skirt the problem of not being able to modify the fundamental frequency, which was previously dominated by the computational block size.

Download

This is a multichannel (surround sound) audio effect which can simulating objects moving through the center of an array of speakers. We included source code, as well as a compiled Max/MSP object for Mac and Windows. This is also a good template for embedding exported Simulink code in Max/MSP if that’s something you’re into. Its inputs are a mono sound source, distance from center and bearing. The sound image sweeps smoothly from the outside of the speaker array, straight through to the other side.

It automatically compensates for amplitude gain, Doppler effect, LF air absorption, reflections and phasing (which can be controlled individually). These are all functions of the distance input, or a derivative thereof. This particular version of the software is using lookup tables to execute those functions. Subsequent versions will most likely compute dynamically in order to allow smooth transitions and avoid other artifacts.

The mirrored panning algorithm takes the processed mono source and copies it into eight channels. It then multiplies those channels with a mask, which isolates the source to those channels which correspond to whatever direction it is coming from. It produces another eight channels using the same mono source, but with 180 degrees added to the bearing. When the distance input gets within a certain range of center, the panner crossfades the original eight channels with the “mirror copy” coming from the opposite direction, allowing the source to transition seamlessly from one side, directly to the other.