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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.111 Introductory Digital Systems Laboratory Problem Set 3 Problem Set Issued: March 3, 2004 Problem Set Due: March 19, 2004 Comments: This problem set is intended to prepare you for Laboratory 3 which is a Finite Impulse Response (FIR) filter. Problem 1 is intended to familiarize you with the concepts of convolution and filtering. While we do not expect you to have a background in signals (6.003 is not a prerequisite) we would like for you to have an appreciation for how digital filtering works. Problem 1: Convolution An FIR filter uses convolution to generate the data points for the filtered output. Convolutions are a weighted accumulation of sampled points from a signal. Given that h[n] is the Finite Impulse response for a specific filter and x[n-k] is the k th recent sample, the equation that best describes the convolution we are going to implement is N 1 y n [ ] [ [ ] = h k x n k ] k = 0 where N is the number of points in the convolution. Given the filter shown below compute the convolution with the following inputs h[n] 5 0 1 2 3 4 1 1 2 2 n Part (a) x1[n] 0 1 2 1 1 n 1 Part (b) x2[n] 0 2 1 1 n -3 Part (c)...
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