To pipeline basic, 1-multiplier, normalized, and scaled-normalized lattice filters by M levels, the denominator of a transfer function is required to have (M − 1) consecutive zero coefficients between each 2 nonzero coefficients of nearest degree. The pipelinable transfer functions can be obtained by applying the scattered look-ahead method to the nonpipelined filter transfer functions. To avoid the drawbacks of the cancelling zeros such as hardware increase and inexact pole-zero cancellations in a finite wordlength implementation, a pipelinable transfer function can also be designed directly from the filter spectrum while the denominator is constrained to be a polynomial in zM rather than z.
In this section, two design examples of pipelined lattice filters are presented. The pipelinable transfer functions have been obtained by the modified Deczky’s method .
pass-band: 0 − 0.2π (0.5 dB) and stop-band: 0.3π − π (20 dB).
The transfer function obtained by the modified Deczky’s method is:
Notice that D(z) can be further decomposed ...