Sunday 28 October 2012

Direct Filters

DirectLowPass, DirectBandPass, DirectHighPass, DirectLowPassBessel, DirectBandPassBessel, DirectHighPassBessel


These six processors represent the work horse of subtractive synthesis and general filtering. They are non resonant infinite impulse response filters with variable cut-off rates. The versions which do not end in Bessel are Butterworth filters. The Bessel ones are Bessel filters. The difference in use is that the Bessel filters introduce hardly any phase distortion in the pass band but are much shallower than the Butterworth filters. The Butterworth filtes do introduce some phase distortion but are much steeper. At the time of writing Sonic Field does not have steeper IIR filters than Butterworth because the lobes in the pass and reject bands of such filters tend to make their use problematic. For a true 'brick wall' style filter convolution is the solution. However, as the Butterworth filters will (under some conditions) go up to 10 or even 11 order and still be stable, it is hard to see why one might want a sharper filter.

High and Low Pass Layout:
(?signal,?frequency,?order)DirectXXXPass !new-signal

Band Pass:
(?signal,?low-frequency,?high-frequency,?order)DirectXXXPass !new-signal

Where XXX is Low,High or Band. Put Bessel on the end of the processor name to get the equivalent Bessel Filter. Frequency is in Hz and order can be from 1 to 11 for low and high or 1 to 5 for band. However, sometimes these filters go unstable and produce non numbers or infinities in the outgoing signal. This is more likely with high pass filters with low frequency cut-offs or band pass where the upper frequency is low or where the two frequencies are very close (closer than 10%). Reducing the order makes it less likely for a filter to go unstable. Low pass filters are almost always stable. High pass are OK at 6 orders down to around 100 Hz and order 2 and 12 Hz (usually). Band pass is less stable and order 4 is only useful for frequencies over 200 Hz. These are all approximate values, experimentation is required.

Note: the higher the order, the steeper the filter. The cut-off frequencies are the -6db points.
 

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