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- | ====== Syllabus ====== | + | ====== Syllabus - ECE 671====== |

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+ | ===== Introduction ===== | ||

+ | The objective of this course is to help you develop the mathematical skills needed to pursue research in the general area of signals and systems. Research topics in this area include (1) signal and image processing (2) communication systems (3) control systems. While there is a lot of hype about the half life of knowledge in electrical engineering being about 2-3 years, the material introduced in the course is timeless, in the sense that the course covers general principles that will never go out of date. The material covered in this course is to signals and systems, what Maxwell's equations are to electro-magnetics and what Newton's laws are to dynamics. During the 60's, 70's and 80's, signal processing and control solutions were usually implemented in analog circuitry. With the advent of powerful computing technology, signal processing solutions are now almost always implemented on a digital computer. The flexibility that comes from programming digital hardware makes it possible to implement algorithms that were impossible to implement in analog circuitry. As this trend continues, efficient algorithm design will become one of the most critical design steps in engineering systems. While the ability to write computer code is important, it does not enable an engineer to design good algorithms. Writing code is similar to the ability to use a word processor. Being able to use a word processor does not guarantee that the writer will produce good prose. Good prose comes from learning the principles of good writing (which have nothing to do with typing). Similarly, if you want to design good algorithms, the kind that make products successful, and that guarantee the engineer a good stable salary, you need to understand the principles of good algorithm design. Many of these principles are mathematical in nature. The objective of this course is teach the mathematical techniques that will allow you to design state-of-the-art signal processing algorithms over the lifetime of your career (a very ambitious objective). | ||

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+ | Many of you will find this course mathematically challenging. There is a great deal of systems engineering that cannot be mastered without some mathematical sophistication. Mathematical maturity can be obtained by anyone willing to work at it. This course offers you an opportunity to refine your mathematical and analytical skills and if you work hard at the material you will be rewarded by increased engineering insight and skill. | ||

===== Learning Outcomes ===== | ===== Learning Outcomes ===== | ||

The objective of the course is to help you develop the following technical skills. | The objective of the course is to help you develop the following technical skills. | ||

- | * | + | * Develop a foundation of basic linear algebra concepts useful in modern signal processing, including vector spaces, norms and inner products, orthogonality, linear operators, matrix inverses, approximations in vector spaces, eigenvalues, and eigenvectors; |

+ | * Understand advanced topics in linear algebra and some of their applications to real-world engineering problems, including important matrix factorization techniques, singular value decomposition, and special matrices and their applications; | ||

+ | * Develop a basic familiarity with the theory of constrained optimization. | ||

===== Text ===== | ===== Text ===== |