Re: [Audacity-devel] New effect - Scientific Filter

[Norm C <n_b...@ho...>]

Yes, I wrote all the algorithmic code myself, derived from the math. Here's a
description, maybe more than you want, but trim as needed:

The Scientific Filter effect implements 3 different types of filters which
together emulate the vast majority of analog filters, and provide useful
tools for analysis and measurement. The three main types are Butterworth,
Chebyshev Type I and Chebyshev Type II. Each of those has two subtypes:
Lowpass and Highpass. These filters (and the analog prototypes on which they
are based) generally pass through a range of frequencies (called the
passband) with minimal attenuation, and the remainder (called the stopband)
with some significant degree of attenuation. The boundary between the
passband and stopband is called the Cutoff Frequency.

Of the 3 types, Butterworth is the simplest. An analog Butterworth filter
provides a "maximally flat" passband (ie. no ripples), the magniture
response at the cutoff frequency is -3 dB, and above (for lowpass) or below
(for highpass) the cutoff frequency, the attenuation increases at
approximately 6 dB per octave times the filter order (so eg. 60 dB per
octave for 10th order). The Scientific Filter approximates this behaviour
very closely, except at very high frequencies (see later). Butterworth
filters are simple to implement in analog; in fact, a voltage source driving
a series resistor which feeds a shunt capacitor is just a 1st order
Butterworth lowpass filter, and if you reverse the resistor and capacitor it
becomes a 1st order Butterworth highpass filter.

Chebyshev Type I filters are similar, except that a) the magnitude response
of the passband has "ripples" in it (usually small), b) at the cutoff
frequency the magnitude response is equal to the ripple value, and c) above
(below for highpass) the cutoff frequency, the stopband attenuation
increases more rapidly, for a given filter order, than Butterworth.

Chebyshev Type II filters are similar to Butterworth, including the flat
passband response, except that a) at the cutoff frequency the magnitude
response is equal to the ripple value, b) above (below for highpass) the
cutoff frequency, the stopband attenuation increases more rapidly, for a
given filter order, than Butterworth, and c) the stopband attenuation varies
from infinite to the ripple value. (Here it's common to use a ripple value
of 20, 30 or more dB).

All three filter types (and both subtypes) are commonly used in analog audio
circuitry. First order Butterworth filters, as mentioned, are extremely
simple. Second to 4th order Butterworth and Chebyshev filters are normally
implemented with opamps or, rarely, inductors and capacitors. Higher order
analog filters are rare, due to the very high component precision that would
be required.

The high-frequency response of all 3 filter types diverges from that of the
analog prototypes, due to the bilinear transformation used in converting
analog to digital filters. Essentially the response at the Nyquist frequency
(sampling frequency divided by 2) in the digital version is equal to the
response at infinite frequency in the analog version. So for lowpass
filters, the attenuation at Nyquist is infinite (for Butterworth and
Chebyshev Type I filters).


Norm




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