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262 Chapter 6 DSP Algorithms
and by iterating L steps ahead we get
where
and
We assume that these matrices can be precomputed and neglect the fact that
the word length of the matrix coefficients increases. Hence, Equation (6.3) can be
iterated with an iteration period that is the same as the original set of state-space
equations, but L output values are computed at each iteration. The effective iteration
bound has therefore been decreased. We define a high-speed digital filter structure
as a structure whose throughput is not bounded by the multiplication cycle time.
Theorem 6.5
The minimum sample period for block processing of an TVth-order state-
space algorithm is
where T mui t + Flog2(-/V+l)l T a(j^ is the total delay (latency) due to the arith-
metic operations and L is the block size.
The number of operations per sample is
where the first term is the number multiplications, the second term is the number
of additions, and N is the filter order.
