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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online