[sdiy] Filter slopes
rburnett at richieburnett.co.uk
Mon Jun 11 10:25:35 CEST 2018
The SVF BP output is "second order" or "two pole". All of the output responses are second order. The transfer functions of all outputs have a denominator polynomial that is 2nd order in 's'. It is the numerator order that changes for LP, BP, HP outputs and it essentially tilts the LP frequency response for increasing powers of 's' to get BP then HP.
Sent from my Xperia SP on O2
---- rsdio at audiobanshee.com wrote ----
>On Jun 10, 2018, at 10:43 PM, Elain Klopke <functionofform at gmail.com> wrote:
>> I was reading an article about the spectral content of various instruments (woodwinds and strings) and while they didn't have any circuits, there were some tables showing cutoff frequencies and high and low slopes. Several of the pictures looked like bandpass filter responses with different slopes on each side. How would I go about doing that? Is the slope determined by the gain of the op amp in an active filter? If it's that easy, would it be a highpass filter followed by a lowpass filter each with their own gain settings?
>Slope is almost always determined by the order (number of poles) of the filter, at least for simple analog filters. 1st order is 6 dB/octave. 2nd order is 12 dB/octave. 4th order is 24 dB/octave. Each order (pole) is usually created by a capacitor (or inductor).
>You can create a bandpass filter by summing a highpass and a lowpass, provided that you carefully coordinate the filter frequencies.
>The slope can be different for each side of the bandpass, which just means that the individual highpass and lowpass filters will have different orders.
>As with most things, there’s more than one way to solve the problem.
>Do these instrument graphs have the slopes marked numerically? I recall that 3 dB/octave (pink noise) is terribly difficult to obtain from an analog filter, so I hope that the slopes of these natural instruments are not difficult to achieve.
>p.s. The common SVF (state variable filter) creates a bandpass, lowpass, and highpass simultaneously, but the lowpass and highpass are second order (12 dB/octave) while the bandpass slope sides are only first order (6 dB/octave). At least I recall there is something about the bandpass that is not as naively expected. A quick search online confirmed the differing slopes for bandpass versus the others, but the provided graph seemed to indicate the opposite (2-pole BP, but 1-pole LP and 1-pole HP) - which might have simply been an error in the graph. Anyway, the SVF can be used to produce a notch filter by summing the LP and HP outputs. Your interest in obtaining different slopes for each side means that you probably shouldn’t use a SVF filter, especially not its BP output, but perhaps just some simpler LP and HP circuits.
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