Outline_Topic 03 - Skip the discussion surrounding equation...

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Outline – Topic 3: Discrete-time Convolution Spring 2007 Topic 3. Discrete-time Convolution Convolution is the basis of filtering. Students generally find this concept to be the most difficult in the course, so plan to spend sufficient time to master it. Two key operations are involved in solving convolution problems: Setting up the limits on the sums, and determining the values of n for which those limits are valid. Representation of Discrete-time Signals in Terms of Impulses. Read Section 2.1.1 We have already dealt with this idea: any discrete-time signal can be represented as a sum of shifted impulses. This section treats the general case. Discrete-time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems. Read 2.1.2 Very important section. Study this section carefully to understand the basic approach.
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Unformatted text preview: Skip the discussion surrounding equation 2.3 and concentrate on page 78. Equation 2.6 is the key. It is a restatement of superposition. We will introduce an array method, not in the text, for handling finite sequence problems. Understand the general graphical approach for setting up the convolution sums and the limits on the sums given in the text examples 2.1, 2.2, 2.3 and 2.4. Study videos 3.1, 3.2, and 3.4. Some of these videos as well as the text examples require summation formulas developed in video 3.3 (See text, problem 1.54, p73). Video 3.4 is a detailed solution for text example 2.4. Start with the problem statement in the text, and try to solve the problem by yourself. Then check your solution and procedure with the one given in the text. If you are still having difficulty, then consult video 3.4....
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