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