Sparse multi-stage loss filter design for waveguide piano synthesis

A new filter structure and a design method are proposed for the loss filter that is used in digital waveguide synthesis. The main application of this work is the sound synthesis of the piano, but the methods are also applicable to the synthesis of other struck or plucked string instruments. The filter structure is an extension of a sparse FIR filter called the ripple filter, which has been proposed previously for waveguide synthesis of keyboard instruments. The new structure is based on a cascade of sparse FIR filters, which are designed one after the other on subbands that are integer fractions of the audio range. We show by examples that a cascade of three digital filters provides possibilities to exactly match the decay rate of a finite number, such as 50, lowest-order partials, or to approximately match the general trend and some variations of many partials of a piano tone. The subfilters can easily be designed using standard techniques