课程名称︰ 数位讯号处理 课程性质︰ 研究所选修 (本试题用於电机所/电子所/生医电子所博士班资格考选考科目) 课程教师︰ 贝苏章 开课学院： 电机资讯学院 开课系所︰ 电信所 考试日期（年月日）︰ 103/4/12 考试时限（分钟）： 100 是否需发放奖励金： 是 （如未明确表示，则不予发放） 试题 : 1. (a) 16% y[n] - y[n-1] = x[n] + x[n-1] What is the impulse response h[n] and step response s[n]? (b) 9% x[n] = (a^n)u[n], find the inverse function h[n] such that x[n]＊h[n] = δ[n] 2. (a) x[n] = (4,-2,4,-2,4,-2,4,-2) Find its 8-point DFT, X[k] (b) x[n] = (x0,x1,x2,x3) and its 4-point DFT X[k] = (A,B,C,D) If x'[n] = (x0,0,x1,0,x2,0,x3,0), find X'[k] (c) Explain radix-2 decimation in time FFT, and radix-2 decimation in frequency FFT 3. Plot the frequency response (magnitude and phase) of H(z) = 0.25 + 0.5z^-4 + 0.25z^-8, using normalized frequency z = e^jπν What type of filter is this? (LPF, HPF, BPF, multi-BPF...) 4. Explain sampling theorem, aliasing, decimation, interpolation, Gibb's phenomenon , and windowing --

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