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Calculating filter coefficient from a transfer function - literature not clear
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rhb:
You are concerned with providing the best match to an arbitrary transfer function  under certain constraints as to performance and cost aren't you?

Matched filter design is routine in seismic and most other DSP environments.  What would you like the spectrum to look like?  Do you just want me to search for that recordings containing that voice spectrum?

Wiener developed all of this around 1940 and later published as "The Smoothing, Interpolation and Extrapolation of Stationary Time Series." in 1949.  In it he presents the convolutional model, one of  the most basic models in mathematical physics.

Candes and Donoho are as big a step change as Wiener and Shannon were.

If you want to look like a genius, learn to formulate and solve problems such as the one you posed via linear programming.  You and all around you will be amazed.  It is the wildest stuff I've ever seen. 

Have Fun!
Reg
Yansi:
Well, I am not trying to best match a transfer function, hence why I don't understand you. I just try understanding, how to make a signal limiter in a DSP (mainly for speaker rms power protection and to prevent peaks from saturating the power amplifier)

And after toying with it for a while, I am finding more and more issues with the systems provided in Zölzer. He has likely just copied from the BBC paper, without even trying to verify.  :-\

I am pretty sure now the AT/RT peak detector system is not working correctly. See below. I am talking about this system, which is supposed to provide signal peak value detection, while respecting a set attack and release time:



More thorough testing with simple waveforms, where the behavior shall be very predictable revealed, that the peak value given in steady state is incorrect:



After poking at it a bit, I see that by providing very short attack times (AT constant is close to 1), the result is correct. So it is also when RT constant is close to 0.
Now thinking about how to patch the system, I am thinking about the feedback path to the |x(n)| subtracting node shall be scaled by some amount.
RoGeorge:

--- Quote from: Yansi on November 30, 2019, 04:52:45 pm ---

I got quite curious about the constant "2.2" in the exponent.

--- End quote ---

Digital came quite late in audio processing.  Before that, it was all analog, so without following too close what is trying to implement there, for sure it's some former analog behavior emulated digitally.  That given said, anything with a time constant in the analog world back then was done with RC circuits.  Looking at the time constant of an RC circuit:

https://en.wikipedia.org/wiki/RC_time_constant

--- Quote from: Wikipedia --- time (10% to 90%) tr ≈ 2.2 τ ≈ 0.35/fc
--- End quote ---

My best guess is that's where from it was coming the 2.2 magic number you were asking about.
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