[sdiy] tanh() and approximations and warping, why is my maths wrong?

[Brian Willoughby]

I have the same question. The frequency warping that I’m familiar with is usually `w = 2*sin(pi * Fc / Fs)`, not tan(), so I’m wondering what filter we’re talking about here.

Brian


On Jun 10, 2019, at 6:56 PM, Andrew Simper <andy at cytomic.com> wrote:
> Which digital filter model is being used that needs pre-warping of the cutoff parameter?
> 
> Andy
> 
> On Tue, 11 Jun 2019 at 04:58, Gordonjcp <gordonjcp at gjcp.net> wrote:
>> On Mon, Jun 10, 2019 at 09:11:58PM +0100, Tom Wiltshire wrote:
>> > I think what he’s looking for is to know why x/(1+x) gives the right warping to get the correct cutoff frequency.
>> > 
>> > Since I know very little of how digital filter models are derived from their analog counterparts and the approximations inherent in that process, I’m not the person to ask…
>> > 
>> > Tom
>> 
>> That's it exactly.  I'm not great at maths and the kind of algebra that
>> goes into this sort of thing is a bit much for me, but x/(1+x) gets the
>> filter tracking absolutely bang on.