Fix aggressive low-end rolloff in DcBlock

[ndonald2]

Description

The current DcBlock implementation in DaisySP is aggressively rolling off low frequencies. This is due to the fixed coefficient of 0.99 being used instead of one dynamically calculated based on the sample rate and approximate target corner frequency.

This change adds a dynamic pole calculation based on an approximate corner frequency of 10Hz at the given sample rate using 1 - fc/fs which is fairly reasonable for corner frequencies below ~100Hz. The exact -3dB corner frequency of the original one-pole lowpass filter can be calculated exactly, but the curve changes when subtracting the filtered signal from the original to achieve a DC-blocking highpass as done here.

For reference, here is the filter amplitude response (at fs = 48kHz) with the original hard-coded pole coefficient of 0.99:

https://www.desmos.com/calculator/ymsix8p9aa

And here is the amplitude response with a dynamic pole coefficient (set initially for a ~10Hz corner freq):

https://www.desmos.com/calculator/uhcegka8st

Note the significant difference - in the first example, there is already an attenuation of about -8dB at 100Hz, which only increases as the frequency gets lower. In the second example, there is only about a -0.7dB reduction at 20Hz which is much more reasonable in terms of the effect on the frequency response of the overall filter acting as a DC Blocker.

Note: the logarithmic display of the desmos graph tool requires a non-zero minimum axis value - set it to linear to see that there is truly infinite attenuation as it approaches DC (0Hz)

Testing

I have been using this code in various projects for quite some time as a remedy for the originally aggressive highpass rolloff from the version with the hard-coded coefficient. The theoretical analysis above also confirms the validity of the change.

For further assurance, a DcBlock could be added to the simple oscillator example for the Seed, noting the reduction in amplitude of the output signal at frequencies < 100Hz in the original version compared to the update.

Finally - comparing the result of the change for a 48kHz sample rate, we get a coef of 1 - fc/fs ~= 0.9997 which is the only effective change to the code. Just a different pole coefficient.

[stephenhensley]

Style CI should be fixed on the master branch, but no need to rebase. I would be flabbergasted if this change failed the CI lol.

Nice catch, and thanks for the thorough PR as always!