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Issue 720009 link

Starred by 1 user
Status: WontFix
Owner: ----
Closed: May 2017
Components:
EstimatedDays: ----
NextAction: ----
OS: ----
Pri: 3
Type: Bug



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Highshelf filter has incorrect gain when cutoff is 0

Project Member Reported by rtoy@chromium.org, May 9 2017 
The implementation of the highshelf filter sets H(z) = A^2 when the cutoff frequency is 0.  However, if you substitute 0 into the formulas, the resulting filter is H(z) = A.

Comment 1 by rtoy@chromium.org, May 9 2017

Status: WontFix (was: Available)
Nope.  If the cutoff frequency is 0, then w0 = 0 and alpha_s = sin(w0)/sqrt(2) = 0.  Then

b0 = A*(2*A) = 2*A^2
b1 = -2*A*(2*a) = -4*A^2
b2 = A*(2*A) = 2*A^2
a0 = 2
a1 = -4
a2 = 2

Then 

  b0+b1/z+b2/z^2 = 2*A^2*(1-2/z+1/z^2) = 2*A^2*(1-1/z)^2
  a0+a1/z+a2/z^2 = 2*(1-2/z+1/z^2) = 2*(1-1/z)^2

Thus, H(z) = A^2.

So, everything is WAI.
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