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Signals and Systems Midterm 9:10a.m. ~ 11:10a.m., May 4, Fri., 2007 z Closed book, but open 1 sheet (both sides, 2 pages) of personal notes of A4 size z Total score: 120 z Total 3 pages in one B4 sheet 1. [10] Consider designing a discrete-time inverse system to eliminate the distortion associated with multipath propagation in a data communication problem, where the propagation channel consists of a direct path and a number of reflected paths. For simplicity, let us consider the discrete-time model of a two-path communication channel depicted as follows: a) [2] Write down the difference equation describing the two-path communication channel system. b) [6] Find the impulse response of a causal inverse system that will recover [ ] x n from [ ] y n . c) [2] Check if the inverse system is stable and explain the physical meaning of the condition you have derived. 2. [12] Consider the signal 7 9 [ ] cos cos . 16 16 x n n n π π = + a) [4] Compute the discrete-time Fourier transform (DTFT) of the signal.

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