VLSI Digital Signal Processing Systems: Design and Implementation

12.8    PIPELINING OF LATTICE IIR DIGITAL FILTERS

Although the lattice filters can be pipelined by the cutset localization procedure, the maximum sample rate of these pipelined filters is limited by the feedback loop computations. For example, in normalized lattice filters, the cutset localization procedure (see Chapter 4) can be applied to transfer one half of each delay on the right directed edges to the left directed edges as shown in Fig. 12.26. The half delays can be implemented by time rescaling. For example, using 1 clock cycle to represent a half delay, we can input 1 sample every 2 clock cycles and generate the output samples once every 2 clock cycles. The maximum sample rate of this structure is limited by the feedback loop computation, which involves 2 multiplications and 2 additions.

Using the Schur algorithm, we show that if the denominator of the transfer function is in scattered look-ahead form, then the transfer function satisfies the pipelining property of lattice digital filters [14],[15]. One drawback of the scattered look-ahead technique is the introduction of the cancelling zeros. These zeros increase the number of multiplication operations needed to implement the digital filter and lead to inexact pole-zero cancellation in fixed point implementations. To avoid the drawback of cancelling zeros, we use pipelined transfer functions designed using constrained filter design approaches. One approach is to use the filter design procedure used for decimation filter ...