Lecture 2 - Introduction to Systems

Lecture 2 - Introduction to Systems - What are Systems? !...

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Lecture 2 Slide 1 PYKC Jan-7-10 E2.5 Signals & Linear Systems Lecture 2 Introduction to Systems ( Lathi 1.6-1.8 ) Peter Cheung Department of Electrical & Electronic Engineering Imperial College London URL: www.ee.imperial.ac.uk/pcheung/teaching/ee2_signals E-mail: p.cheung@imperial.ac.uk Lecture 2 Slide 2 PYKC Jan-7-10 E2.5 Signals & Linear Systems What are Systems? ! Systems are used to process signals to modify or extract information ! Physical system – characterized by their input-output relationships ! E.g. electrical systems are characterized by voltage-current relationships for components and the laws of interconnections (i.e. Kirchhoff’s laws) ! From this, we derive a mathematical model of the system ! Black box ” model of a system: SYSTEM MODEL L1.6 Lecture 2 Slide 3 PYKC Jan-7-10 E2.5 Signals & Linear Systems Classification of Systems ! Systems may be classified into: 1. Linear and non-linear systems 2. Constant parameter and time-varying-parameter systems 3. Instantaneous (memoryless) and dynamic (with memory) systems 4. Causal and non-causal systems 5. Continuous-time and discrete-time systems 6. Analogue and digital systems 7. Invertible and noninvertible systems 8. Stable and unstable systems L1.7 Lecture 2 Slide 4 PYKC Jan-7-10 E2.5 Signals & Linear Systems ! A linear system exhibits the additivity property: ! It also must satisfy the homogeneity or scaling property: if then ! These can be combined into the property of superposition : ! A non-linear system is one that is NOT linear (i.e. does not obey the principle of superposition) Linear Systems (1) L1.7-1
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Lecture 2 Slide 5 PYKC Jan-7-10 E2.5 Signals & Linear Systems ! Consider the following simple RC circuit: ! Output y(t) relates to x(t) by: ! The second term can be expanded: ! This is a single-input, single-output (SISO) system. In general, a system can be multiple-input, multiple-output ( MIMO ).
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Lecture 2 - Introduction to Systems - What are Systems? !...

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