HOMEWORK_9

# 1 1 1 2 2 1 1 1 1 2 1 1 fromtable 2 2 2 cos 3 2 2

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Unformatted text preview: ermine the inverse transform of z ( z + 1) ( z − 1)( z 2 − z + 1) By the following methods: (a) Partial fraction expansion. 1 1 1 2 2 1 1 1 1 2 1 1 From table: ∆ 2 2 2 cos 3 2 2 2 1 1 1 0.5 1 cos ∆ 2 cos ∆ cos ∆ (b) Long division. 1 1 1 3 1 2 2 √ 2 3 3 2 2 6 4 4 6 5 8 3 3 3 3 8 5 6 4 4 6 2 2 3 3 2 ∆ ∆ 3 ∆ ∆ 3 4 7∆ ∆ 3 2∆ 4 0 ∆ 3∆ 3 ∆ 4∆ ∆ 5∆ 4 3 0 2 1 2 1 2 2 1 4 3 1 ∆t 2∆t 3∆t 4∆t 5∆t 6∆t 7∆t 8∆t 9∆t 10∆t 11∆t 12∆t 4. Calculate the z‐transform of the rectangular pulse shown in the drawing. Assume that the sampling period is Δt = 2 min. The pulse is f = 3 for 2 ≤ t < 6. For ∆ 2 : at ∆ 2 1 the sampled value is 3 at ∆ 4 2 the sampled value is 3 3 the sampled value is 0 (f = 3 for 2 ≤ t < 6) at ∆ 6 4 the sampled value is 0 at ∆ 8 The sampled values: 3 1 ∆t 2∆t 3∆t 4∆t 0· 3 3 3 3 0· 5. The pulse transfer function of a process is given by 5( z + 0.6) Y ( z) =2 X ( z ) z − z + 0.41 (a) Calculate t...
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