Difference between revisions of "Course Outline" - Rhea

@@ Line 1: / Line 1: @@
-===Course Outline===
-I. Introduction
-*Review of course policies
-*Why linear systems theory is important
-II. Signals [OW 1.0-1.4]
-*Types - continuous time, discrete time, and digital [OW 1.0-1.1]
-*Transformations of the independent variable [OW 1.2]
-**Time reversal
-**Time delay
-**Time scaling
-*Signal Properties
-**Periodic signals
-**Even/odd signals
-**Energy
-** Power
-** Average value
-*Exponential Signals [OW 1.3]
-**Continuous time
-**Discrete time
-*Impulse and step functions [OW 1.4]
-**Discrete time
-***Relationship between impulse and step functions
-***Representation of DT signals with DT impulses (Sifting Prop.)
-**Continuous time
-***Deﬁnition of CT impulse [OW 2.5]
-***Relationship between impulse and step functions
-***Representation of CT signals with CT impulses (Sifting Prop.)
-III. Systems [OW 1.5-1.6]
-*Input/output models for systems [OW 1.5]
-*System Properties [OW 1.6]
-**Review of formal logic [From notes/handouts]
-**Continuous time and Discrete time systems
-**Causal and noncausal systems
-**Memory and memoryless systems
-**Linear and nonlinear systems
-**Time varying and time invariant systems
-**Stable and unstable systems
-**Formal deﬁnitions of system properties
-IV. Linear Time-Invariant Systems [OW 2.0-2.4]
-*Time domain analysis of linear systems [OW 2.0]
-**Discrete time systems [OW 2.1]
-***impulse function and impulse response
-***discrete time convolution
-**Continuous time [OW 2.2]
-***impulse function and impulse response
-***continuous time convolution
-*Properties for LTI systems [OW 2.3]
-**Memoryless
-**Causal and anticausal
-**Stable
-*LTI analysis of linear diﬀerential equations [OW 2.4]]
-*Complex exponential inputs to LTI systems [OW 3.2]
-V. Frequency Analysis
-*Orthonormal Tranforms [From notes]
-**General analysis of orthonormal transformations
-**Functions as vectors
-**Innerproducts on functions
-**Parseval’s theorem for orthonormal transforms
-*Continuous time Fourier series (CTFS) [OW 3.0-3.3,3.5,3.8-3.9]
-**Derivation as orthogonal transform [OW 3.0-3.3]
-**CTFS examples
-**Properties of CTFS [OW 3.5]
-**LTI system analysis using CTFS [OW 3.8,3.9]
-*Overview of transforms we will cover [From notes and handout]
-*Continuous time Fourier transform (CTFT) [OW 4.0-4.8]
-**Derivation of tranform [OW 4.0-4.1]
-**The convolution property and LTI systems [OW 4.4]
-**CTFT properties [OW 4.3]
-**Transform pairs for aperiodic signals [See OW 4.6]
-**CTFT of periodic functions [OW 4.2]
-**Transform pairs for periodic signals [See OW 4.6]
-**Impulse train sampling [OW 7.1.1]
-**Systems characterized by linear diﬀerential equations [OW 4.7]
-*The DFT [OW 3.6-3.7]
-**Derivation as orthogonal transform [From notes and OW 3.6]
-**Example transforms
-**DFT properties and circular convolution [OW 3.7]
-*Discrete time Fourier transform (DTFT) [OW 5.0-5.1,5.3-5.6,5.8]
-**Tranform deﬁnition [OW 5.0,5.1]
-**DTFT properties [OW 5.3]
-**Transform pairs [See OW 5.6]
-**The convolution property and LTI systems [OW 5.4]
-**Systems characterized by linear diﬀerence equations [OW 5.8]
-VI. Sampling and reconstruction [From Notes, OW Chapter 7]
-*Overview of sampling systems [OW 7.0]
-*Sampling
-**Relationship between CTFT and DTFT
-**Aliasing and the Nyquist frequency
-*Reconstruction
-**Relationship between DTFT and CTFT
-**Aliasing and reconstruction ﬁlters
-**Zero order sample and holds
-VII. (Didn’t get to this) The Z-Transform [OW 10.0-10.7]
-*Deﬁnition of Z-transform
-*Region of convergence
-*The inverse Z-transform
-*More on the Z-transform
-**Left and right hand signals
-**Stable and unstable signals
-**Causal and anticausal signals
-**Z-transform properties
-*Analysis of DT systems
-**FIR systems
-**IIR systems
-**Stability analysis
-[OW ] - Refers to Oppenheim and Willsky text

Difference between revisions of "Course Outline" - Rhea

Latest revision as of 15:58, 22 November 2009

Alumni Liaison