3 layer Discrete Wavelet Transform. The wavelet transform works by multiresolution analysis. This means that the first layer is comprised of the highest energy, most 'detailed' bits of the signal, preceeding the second and third layers. the IDWT is the sum of the recomposition of each of these layers by way of zero-crossing dependent windowed wavelets. each layer can have its own settings for wavelet recomposition, to ensure maximum rendering quality. that's also why certain elements of the sound are left intact while others can be totally dismantled. the filter banks work thusly:
a signal is fed into the 'layer one' filter, which splits it at a frequency using DIR filters (digital High/Low pass). the more 'detailed', highpassed signal is sent to the 'layer one' buffer. the less detailed result of the low pass filter is bit-reduced by a factor of 2 and send to the 'layer two' filter, where the same thing happens. additionally for the third layer. so each layer progressively gets a more general curvature of the sound.
the three buffers are then indexed into using grains whose sizes are dependent on the number of zero-crossings in each grain. at this point, the number of zero-crossings per grain, the number of grains permitted at one time, and the time smear of the grain selection are independently controllable for each layer.
this recording is basically a test of the transform. it is also a test of the composer in sound design, to tune the system appropriately for the materials. many factors go into getting the most effective resynthesis.
the piece itself is something i did a while ago using a limited gamut of events placed into rhythmic patterns that divide an accented beat into unusual numbers of pulses. this piece switches from 5 to 7 pulses per beat, but keeps the cycle the same number of pulses. so basically a poeticized version of the following truth: 5*7=7*5=35 .
