First-Order Allpass Filter

Transfer function:

$$H_1(z) = S_1(z) \mathrel{\stackrel{\Delta}{=}}\frac{k_1+z^{-1}}{1+k_1z^{-1}}$$

(a)

Direct form II filter structure

(b)

Two-multiply lattice-filter structure

Nested allpass filter design:

• Any delay-element or delay-line inside a stable allpass-filter can be replaced with any stable allpass-filter
• More generally, any stable allpass can be replaced by any another stable allpass