Hi Uli,
have you solved the RLB filter problem in between?
It looks as if the a coefficients have exactly the values they should
have if they were not normalized to b0.
Cheers,
Thomas
Am 26.04.2011 08:13, schrieb Uli Brueggemann:
Hi,
I'm wondering about the RLB filter coefficients of ITU1770. They are
clearly specified for a samplerate of 48 kHz.
For other samplerates ITU expects the same shape of curve.
So for computing the coefficients for other samplerates of course a
good way is to reconstruct a IIR filter from the given coefficients.
An example can be found at
http://www-public.tu-bs.de:8080/~y0035293/ITU-R-BS.1770-1-filters.pdf
The method decribed here works very well for the prefilter.
But it seems that the RLB filter cannot perfectly be described by a
biquad IIR filter.
You can simply check this: ITU1770 defines the coefficient values
a0 = 1, b0 = 1, b1 = -2 and b2 = 1
Indeed the parameters high-pass gain factor Vh = 1, band-pass gain
factor Vb = 0 and low-pass gain factor Vl = 0 fit to the equations for
b0, b1 and b2.
But the equation
a0 = 1 = 1 + K/Q + K^2 requires that
K^2 = -K/Q
With K <> 0 (K=0 would not make sense, fc would be 0) we get
K = -1/Q
but a negative value for K also does not make sense.
Indeed using the data Vh, Vb, Vl, Q, Omega=K as published do not
exactly lead to the published filter coefficients, we get deviations
of up to 0.5%.
You may check out by yourself the formulas of the Audio EQ Cookbook.
You will step into the same problem.
So IMO the given RLB filter cannot be described by a biquad IIR filter
under aspects of perfect accuracy.
Which IIR filter will exactly fulfill the conditions specified by the
ITU 1770 RLB filter coefficients?
Uli
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