# First order Allpass function

I have need of the coefficients to use in the biquad-m to implement a first-order allpass filter.
What I want to do is similar to a Hilbert Transform.
There is a sequence of first-order allpass filters:
One is called “P” for positive, with 45 degree relative phase sift
the other is called “N” for negative 45 degrees relative phase shift.
This differential phase shift makes the two sounds orthogonal.
And this orthogonality is held by the phase errors of the relative signals to be less than 1 degree across the information band
That band can be as small as 11:1 and as large as >1000:1, depending on the complexity.
Of course, the phase shift is relative to each other at the end of the filtering.
Classically they are used in single sideband radios to directly modulate the upper or lower sideband as needed
Even though there are other ways to do such things, this is the desired method considering where the Nyquist frequency is in relation to the information band.
— I feel sorta stupid that I haven’t been able to derive this very simple question of the coefficients to the biquad-m construct.
I know that A2 and B2 are zeros as it is a first-order transfer function in Z
So I just need to know what is the warped value of freq that is used for A1
… And the coefficients for B0 and B1 to realize the first order allpass filter.
Surprisingly MatLab is silent about this, probably because the first order allpass filter is deemed too trivial to be of much use.