From: Norm C <n_badger42@ho...>  20131002 02:51:57

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 highfrequency 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  View this message in context: http://audacity.238276.n2.nabble.com/NeweffectScientificFiltertp7559667p7559711.html Sent from the audacitydevel mailing list archive at Nabble.com. 