Consider an LTI system described by the following block diagram The overall

Consider an lti system described by the following

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Consider an LTI system described by the following block diagram The overall system function can be computed as 4-May-19 EIE3001 Sig & Sys, Spring 2019 39 * We have used the convolution property and linearity property to arrive at the result.
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Example 1: First-order System with a Feedback Loop Consider a causal LTI system with the following system function Method 1: Use the formula from the previous slide, which yields H 1 ( z ) = 1, 4-May-19 EIE3001 Sig & Sys, Spring 2019 40
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Example 1: First-order System with a Feedback Loop Consider a causal LTI system with the following system function Method 2: First compute the difference equation in time domain Then the diagram follows 4-May-19 EIE3001 Sig & Sys, Spring 2019 41
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Example 2: System with Both Forward and Feedback Consider a causal LTI system with the following system function This system can be considered as the cascade of two systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 42
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Example 2: System with Both Forward and Feedback Consider a causal LTI system with the following system function This system can be considered as the cascade of two systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 43
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Example 3: Second-order System Consider a causal LTI system with the following system function Method 1: Direction inspection. First obtain the difference equation and then rearrange the terms: 4-May-19 EIE3001 Sig & Sys, Spring 2019 44
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Example 3: Second-order System Consider a causal LTI system with the following system function Method 2: Cascade method. From the system can be considered as the cascade of two first-order feedback systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 45
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Example 3: Second-order System Consider a causal LTI system with the following system function Method 2: Cascade method. From the system can be considered as the cascade of two first-order feedback systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 46
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Example 3: Second-order System Consider a causal LTI system with the following system function Method 3: Parallel-form. Apply partial series expansion the system can be considered as the linear combination of two first-order feedback systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 47
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Summary ¾ Expected learning outcome Understand the relationship between z-transform and DTFT Be able to represent discrete-time signals using z-transform Be able to apply the properties of z-transform Be able to compute inverse z-transform using inspection and partial-series expansion techniques Be able analyze LTI systems using z-transform ¾ Suggested reading: Sections 10.1—10.3, 10.5—10.8. 4-May-19 EIE3001 Sig & Sys, Spring 2019 48
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