Re: [Audacity-devel] Classic Filters status

[Federico M. <fm...@fc...>]

Steve,

Your examples are good, but I just would like to add some comments.

> Nevertheless, digital implementations of Butterworth filters are still 
> very widely used in audio production (for example, for rolling off low 
> bass in microphone recordings).

This is an example of a "vintage" application. With a digital filter it 
is possible to perfectly compensate, at a given distance (which could be 
an input parameter), the proximity effect. Butterworth cannot do that; 
moreover, microphone hardware roll-off usually features a single cutoff 
frequency. As regards to just removing rumble or low frequency hum, any 
linear phase FIR filter can do a better job over the pass band.

What I mean is that Butterworth is a valid choice but not the only one, 
and not even the best.

> Sinc filters are useful in audio production to avoid aliasing 
> distortion (for example, when speeding up a recording).

Correct, but note that it is impossible to get a true sinc filter, they 
are always windowed sinc, so some amount of aliasing is to be present. 
Chebyshev can be used with the same purpose since it attains a very fast 
roll-off close to the Nyquist limit with a smaller order.

Maybe the order seems unimportant but it could matter in real time 
applications. In analog breadboard circuit, order is equivalent to 
component count. In the digital counterpart, high order means inefficiency.

Matlab uses, for the purpose of resampling, a filter based on the Kaiser 
window. Probably this is more computationally efficient than the sinc 
filter (though, arguably, any nearly brick-wall filter may be called a 
sinc filter...)

> Digital implementations of Linkwitz-Riley filters may be used for 
> splitting out an LF channel for multi-channel audio.

Linkwitz-Riley is frequently two Butterworth LP in cascade and two 
Butterworth HP in cascade. The interesting thing is that time alignment 
could be easilly accomplished by means of a simple delay (which could be 
required as a parameter). What cannot be accomplished is perfect 
equalization of loudspeaker frequency response, so often L-R is just a 
theoretical ilusion.

> It seems a simple and obvious question, but so far no-one has provided 
> an answer - why would I choose to use a Chebyshev filter rather than 
> any other type of filter? (clearly, component count for hardware 
> implementation is irrelevant in Audacity). It bothers me that we are 
> considering adding a feature for which there is apparently no 
> practical use.

I think we shouldn't pose the quest in terms of "rather than any other", 
since the perfect filter for a given application doesn't exist. It 
suffices that there be some situations where the choice is a valid option.

The most obvious one is to simulate, not a circuit (for which, as you 
say, there are many circuit simulators), but the /behavior/ of the 
circuit or system, for instance an antialiasing filter or a highly 
selective bandpass filter as some used in spectrum analyzers. Now that 
you have mentioned Linkwitz-Riley, Chebyshev is one of the possible 
alignments in Thiele-Small theory of loudspeaker vented boxes. See, for 
instance, this paper by Richard Small: 
http://diyaudioprojects.com/Technical/Papers/Vented-Box-Loudspeaker-Systems-Part-IV.pdf

I hope you finally consider that this may be a start for an answer to 
your question.

>> As I wrote previously, I can completely see why we would want to 
>> include the Chebyshev filters in SPICE software, but I still don't 
>> know the answer to the audio production question "when and why should 
>> I use a Chebyshev filter?" For most effects the manual says why/when 
>> an effect would be used - a typical job - we still don't have that 
>> for Chebyshev filters.

Audio production may be the main intended application of Audacity, but 
it isn't the only one.

> Surely there is much better software for analog circuit simulation, 
> for example: 
> http://en.wikipedia.org/wiki/List_of_free_electronics_circuit_simulators

Circuit simulators are not intended for simulating a mathematical 
formula, but to include in the analysis the full range of non-idealities 
of real-life components, including nonlinear behavior, thermal effects, 
electrical noise, Montecarlo analysis of tolerance and so on. On the 
other hand, this horse power is very time-consuming, so it may take 
quite long to simulate the effect on several minutes of audio. Circuit 
simulators excel in computing the frequency response, the noise 
behavior, distortion and so on.

Regards,

Federico