EL ENG 120 Study Guide - Midterm Guide: Advanced Format, Parameterized Complexity, Unit Circle
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1. (20 points) the following values from the 8-point dft of a length-8 real sequence x[n] are known: Hint: derive a general formula that relates w [k] to x[k] so you don"t have to calculate x[n] and w[n]. (sam) a). X[1] = x [7] = 2. 5 + 7j. X[3] = x [5] = 3. 5 3. 5j. X[6] = x [2] = 0. 5 + 4. 5j x[0] = X[k] (3 + 2( 2. 5) + 2(0. 5) + 2(3. 5) + 5) W [1] = x[2] = 0. 5 4. 5j. W [3] = x[6] = 0. 5 + 4. 5j (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 1: (20 points) when the input to an lti is: the output is: x[n] = ! 2"n u[n] + 2nu[ n 1] y[n] = 6! Is it stable: (5 points) write the di erence equation that characterizes the system. (sam) a). 4 z 1 (14) (15) (16) (17) (18) (19) (20)
