課程名稱︰ 數位訊號處理 課程性質︰ 研究所選修 (本試題用於電機所/電子所/生醫電子所博士班資格考選考科目) 課程教師︰ 貝蘇章 開課學院： 電機資訊學院 開課系所︰ 電信所 考試日期（年月日）︰ 103/4/12 考試時限（分鐘）： 100 是否需發放獎勵金： 是 （如未明確表示，則不予發放） 試題 : 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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