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The coefficient a is related to cutoff frequency fc and sample rate fs by:
[ H(z) = \fraca + z^-11 + a z^-1 ]
Where ( a ) is the coefficient determining the cutoff frequency. The magnitude ( |H(z)| = 1 ) for all ( z ), but the phase ( \angle H(z) ) shifts from 0 to -180 degrees (or 0 to -360 degrees for second-order filters). To understand allpassphase, you must understand group delay —the derivative of phase with respect to frequency. Group delay measures the time delay each frequency component experiences as it passes through a system. allpassphase
[ H(z) = \fraca_2 + a_1 z^-1 + z^-21 + a_1 z^-1 + a_2 z^-2 ] The coefficient a is related to cutoff frequency
For a allpass (more phase shift and steeper group delay peak), the transfer function becomes: Group delay measures the time delay each frequency