Questions like these probably belong on the music dsp mailing list.

http://musicdsp.org/

Not saying people here don't know the correct answer, but there are
probably more people there that can have the discussion.

By the way if you really want to know how Audacity works under the hood you
could just go and look at the source code:

http://www.audacityteam.org/community/developers/#git

On Wed, Feb 8, 2017 at 8:17 AM, Evan Balster <[email protected]> wrote:

> Whoop, meant to send this reply to the list:
>
> A filter's transfer function simultaneously describes its response to a
>> one-sample impulse *and* its response to any complex frequency in the
>> z-domain.  There's no need to compromise.
>> The reason for this?  Applying a filter to a signal is the same as
>> convolving the signal by the filter's impulse response.  Convolution in the
>> time domain, as exemplified by filters, is identical to multiplication in
>> the frequency domain.  Thus we can look at any point in the transfer
>> function (as evaluated in the z-domain) and derive the effect the described
>> filter will have on that frequency.
>
>
> To expand on that:  When we graph the filter response, the transfer
> function is what's getting graphed.  A magnitude chart depicts the
> logarithm of the transfer function's magnitude for e^(iw) where w is
> angular frequency; a phase chart depicts the imaginary part of the
> logarithm.
>
> – Evan Balster
> creator of imitone <http://imitone.com>
>
> On Tue, Feb 7, 2017 at 10:10 AM, Roman Thilenius <[email protected]>
> wrote:
>
>>
>>
>> isnt that exactly the same as sending a stream of one spike into the
>> filter?
>>
>> i am just not so sure if the transfer function itself really describes
>> the "response curve" best. :)
>>
>>
>>
>> On Jan 17, 2017, at 6:30 PM, Evan Balster wrote:
>>
>> I must disagree.  The cleanest way to compute the transfer function, is
>>> to compute the transfer function, directly — you'll get an exact answer,
>>> with minimal computational expense.
>>>
>>
>>
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