Digital Signal Processing Systems, Basic Filtering Types, and Digital Filter Realizations - Digital Signal Processing: Fundamentals and Applications - page 194

(a)

(b)

(c)

FIGURE 6.22

(a) Direct-form I realization; (b) direct-form I realization with M ¼ 2; (c) notation.

Also, if we define a new z-transform function as

XðzÞ

WðzÞ¼ (6.31)

1 þ a 1 z 1 þ/þ a M z M

we have

YðzÞ¼ðb 0 þ b 1 z 1 þ/þ b M z M ÞWðzÞ

(6.32)

The corresponding difference equations for Equations (6.31) and (6.32) , respectively, become

wðnÞ¼xðnÞa 1 wðn 1 Þa 2 wðn 2 Þ/ a M wðn MÞ (6.33)