Time-Varying Filters for Musical Applications

A variety of methods are available for implementing time-varying digital filters for musical applications. The considerations for musical applications differ from those of other applications, such as speech coding. This domain requires realtime parametric control of a filter such as an equalizer, allowing parameters to vary each sample, e.g. by user interaction, a low-frequency oscillator (LFO), or an envelope. It is desirable to find a filter structure that is timevarying stable, artifact-free, computationally efficient, easily supports arbitrary filter shapes, and yields sensible intermediate filter shapes when interpolating coefficients. It is proposed to use the state variable filter (SVF) for this purpose. A novel proof of its stable time-varying behavior is presented. Equations are derived for matching common equalizer filter shapes, as well as any zdomain transfer function, making the SVF suitable for efficiently implementing any recursive filter. The SVF is compared to state of the art filter structures in an objective evaluation and a subjective listening test. The results confirm that the SVF has good audio quality, while supporting the aforementioned advantageous qualities in a time-varying digital filter for music. They also show that a class of time-varying filter techniques useful for speech coding are unsuitable for musical applications.