Explicit formulas for lattice wave digital filters

A Systematic Algorithm for the Synthesis of Multiplierless Lattice Wave Digital Filters

“…It should be pointed out that, in addition to adders and/or subtracters needed for the adaptor coefficients, several structural adders are also required for implementing the wave-digital allpass sections. These first-and second-order wave-digital all-pass sections are constructed based on the use of two-port adaptor structures and delays as depicted in Fig 2. For LWD filters, there exists a great variety of adaptor structures according to the realization possibilities of the analog reference filters (Fettweis, 1986;Fettweis et al, 1974;Gazsi, 1985). The actual multipliers to be implemented and the number of structural adders required to implement the two-port adaptor structures depends on the selected adaptor type.…”

“…The actual multipliers to be implemented and the number of structural adders required to implement the two-port adaptor structures depends on the selected adaptor type. Figure 6 shows particular symmetric two-port adaptor structures that lead to the optimal scaling for a sinusoidal excitation according to the discussion in (Gazsi, 1985). However, it has been shown, based a further study performed in (Renfors & Zigouris, 1988), that in some cases for the second-order wave-digital all-pass sections, the additional scaling factors c and 1/c are required at the input and the output of the second adaptor, respectively, in order to achieve the optimal scaling.…”

“…Efficient two-port adaptor structures yielding optimal scaling for a sinusoidal excitation (Gazsi, 1985).…”

“…If the A 1 (z)'s are expressible in terms of the adaptor coefficients as follows [see, e.g., (Gazsi, 1985)]:…”

“…Figure 2 shows the realization for a low-pass sub-filter transfer function H k (z), where the firstand second-order sections of (2a) and (2b) are implemented as a cascade of first-and secondorder wave-digital all-pass structures, out of which the best ones for the main purposes of this book chapter will be considered in detail in Section 3. In the high-pass case, the corresponding transfer function is obtained by simply changing the (Gazsi, 1985). In the band-stop case, M 1 are two times an odd integer and an even integer, respectively, and M…”