Main Content

Convert coupled allpass filter to transfer function form

`[`

returns the vector of coefficients of `b`

,`a`

] = ca2tf(`d1`

,`d2`

)`b`

and `a`

.
`b`

and `a`

corresponds to the numerator and the
denominator of the transfer function *H(z)*, respectively, where
`d1`

and `d2`

are real vectors corresponding to the
denominators of the allpass filters *H1(z)* and
*H2(z)*.

$$H(z)=B(z)/A(z)=\frac{1}{2}\left[H1(z)+H2(z)\right]$$

`[`

returns the vector of coefficients `b`

,`a`

] = ca2tf(`d1`

,`d2`

,`beta`

)`b`

and the vector of coefficients
`a`

corresponding to the numerator and the denominator of the transfer
function *H(z)*, respectively, where `d1`

and
`d2`

are complex vectors and `beta`

is a complex
scalar.

$$H(z)=B(z)/A(z)=\frac{1}{2}\left[-(\overline{\beta})\cdot H1(z)+\beta \cdot H2(z)\right]$$

`[`

also returns the vector of coefficients `b`

,`a`

,`bp`

] = ca2tf(`d1`

,`d2`

,`beta`

)`bp`

of real or complex
coefficients that correspond to the numerator of the power-complementary filter
*G(z)*, where `d1`

and `d2`

are
complex vectors and `beta`

is a complex scalar.

$$G(z)=Bp(z)/A(z)=\frac{1}{{2}_{j}}\left[-(\overline{\beta})\cdot H1(z)+\beta \cdot H2(z)\right]$$

[1] Vaidyanathan, P. P., and Sanjit K.
Mitra. *Robust Digital Filter Structures: A Direct Approach*. IEEE
Circuits and Systems Magazine 19, no. 1 (2019): 14–32.
https://doi.org/10.1109/MCAS.2018.2889204.

[2] Vaidyanathan, P. P.
*Multirate Systems and Filter Banks*. Prentice-Hall Signal Processing
Series. Englewood Cliffs, N.J: Prentice Hall, 1993.

`cl2tf`

| `iirpowcomp`

| `tf2ca`

| `tf2cl`