Re: [Audacity-devel] Classic Filters status

[Steve t. F. <ste...@gm...>]

On 2 January 2015 at 21:52, Steve the Fiddle <ste...@gm...> wrote:
> On 2 January 2015 at 19:24, Federico Miyara <fm...@fc...> wrote:
>>
>> Steve,
>>
>> That makes sense where component count, physical size and
>> manufacturing costs of analog filters are relevant, but surely it is a
>> spurious trade off for digital filters. Yes a 2nd order Chebyshev
>> filter may have a slightly steeper roll-off compared with a second
>> order Butterworth, (at the expense of ripple in either the pass band
>> or stop band), but for digital filters there is absolutely no need for
>> that compromise - if you want a steeper roll-off, use a higher order
>> Butterworth filter and then you get a steeper roll-off with no ripple.
>>
>>
>> Higher order in Butterworth means more phase distortion (as in any analog
>> filter), what in turn means worse transient response (for instance, more
>> ringing. It ios true that for the same order Chebyshev is worse than
>> Butterworth, but a Butterworth of larger order has worse transient behavior,
>
> Sorry but that is just not true, but it does demonstrate the point
> that including Chebyshev filters makes the effect too complicated and
> confusing for the vast majority of users (including many very
> experienced users).
>
> Buterworth filters have a more linear phase response in the pass band
> than either type I or type II Chebyshev filters. A type 1 Chebyshev
> low pass filter will ring more at frequencies a little below the
> corner frequency than a Butterworth filter, and a type 1 Chebyshev
> high pass will ring more at frequencies a little above the corner
> frequency than a Butterworth filter.
>
> Type 2 Chebyshev filters ring less near the corner frequency, but at
> the expense of significantly worse roll-off characteristics and
> stop-band performance.
>
> Stephen Butterworth owes his immortal fame to finding the sweet spot
> between type I and type II, where an IIR filter of a given order most
> closely resembles the ideal high/low pass.
> http://en.wikipedia.org/wiki/Butterworth_filter
>
> Attached is a screen shot demonstrating the ringing effect of a 4th
> order Butterworth high pass filter compared with 3rd order Chebyshev
> type I and type II filters on a 2 ms noise pulse (Waveform (dB) view).

For completeness, I've attached a "Spectrum (log f)" view of the same
impulses to illustrate the low frequency roll-off of the different
filter types.

Steve


>
> Steve
>
>>
>> Regards,
>>
>> Federico
>>
>>