Computer Sound Synthesis 2 MUS_TECH 335 Selected Topics

Filters continued

Temporal Response of Filters The temporal response of a filter can be conceptually divided into a transient response and a steady-state response. The steady-state response is the temporal behavior of the filter in the presence of a continuous, constant sinusoidal input.

Transient Response The transient response is how the filter behaves in response to changes in the input. The impulse response is one way of conceptualizing the transient behavior of a filter. This is probably the most important for us. The other kind of transient response that is often discussed is the step response, that is, how the filter behaves in response to a step function input.

Transient Response For FIR filters, the impulse response is as long as the order of the filter plus 1. For IIR filters, the impulse response is infinite and decays exponentially. one-pole filter two-pole filter

Transient Response By convention the decay time is defined like reverberation time to be the time required for the signal to decrease amplitude by 60 dB. t a db

Transient Response of 2-Pole Filter The decay time of a 2-pole filter increases with Q. t a high Q low Q

Physical Analogies The impulse response of a two-pole filter is analogous to the response of a physical resonator to an impulsive input or the response of a resonating bar to an impulsive strike. t a 0 1.0

Formlet Filters Formlet filters are a modified form of resonator with an attack time as well as a decay time. This is done by subtracting the output of one 2-pole filter from another. t a attack decay

Physical Analogies The acoustics of notes on many percussive instruments can be viewed in terms of a summation of sinusoids each of which has an exponential decay. Metal bars, wooden bars, bells, gongs, Tibetan bowls, crystal bowls, etc. have this behavior. They are also sound sources in which the partials are not harmonic. The distribution of the partials is a cue to the kind of material the object is made of. Bells often have a ‘strike tone’ with a quick decay and a sustained part with a long decay. This is part of the ancient ‘technology’ of bell making.

These systems can be simulated by a bank of resonators f 2-pole etc.

More on Physical Analogies Beside the behavior of striking that can be often approximated by an impulse, continuous actions like rubbing, scraping or can be approximated by using low-frequency noise as an input. The temporal quality of the various noise generators gives each a distinctive character. Each of the filters in the filter bank is responding to the part of the noise in its own frequency band and therefore each filter has an independent temporal response.