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Algorithms and Parallel Computing by Fayez Gebali

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12.4 z-DOMAIN ANALYSIS OF 1-D IIR DIGITAL FILTER ALGORITHM

The z-domain 1-D IIR digital filter algorithm is obtained from Eq. 12.1 as

(12.28) c12e028

where X and Y are the z-transform of the signals x(n) and y(n), respectively, and b(0) = 0. We can think of Eq. 12.28 as a polynomial expression in the different powers of z−1. By using different polynomial evaluation techniques, the filter expression is converted to a set of recursive expressions that can be evaluated using a processor array or multiple software threads.

12.4.1 Design 3: Broadcast Inputs and Pipelined Output

Apply Horner’s’ scheme to Eq. 12.28 to obtain the recursive expression

(12.29) c12e029

The above equation can be written as

(12.30) c12e030

(12.31) c12e031

(12.32) c12e032

(12.33) c12e033

Based on the above iterative expression, task T(i) computes Yi in Eq. 12.30 using one multiplication and one addition:

(12.34)

The output of T(i) is buffered ...

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