1. Digital Signal Processing Solutions to Final 2013 Edited by Yang-Ting Justing Chou Confirmed by Prof. Jar-Ferr Kevin Yang LAB: 92923 R, TEL: ext. 621 E-mail: yangting115@gmail.comyangting115@gmail.com Page of MediaCore: http://140.116.92.181http://140.116.92.181

2. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan Announcement Final Exam: 繁城, 9:10~11:30, 01/10 Course Website: http://140.116.92.181/dsp.htm –Homework –Past Examinations TA E-mail: yangting115@gmail.comyangting115@gmail.com TA Time: Wednesday, 10-11 am. HW#7 & HW#8 Submission: 23:59, 01/14 2016/3/102

3. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 2016/3/103 1.1 ( a ) Explanation

4. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 2016/3/104 1.1 ( b ) Explanation

5. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 1.1 ( c ) Explanation 2016/3/105

6. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 1.1 ( d ) Explanation 2016/3/106

7. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 1.2 Auto-Correlation Function (ACF) Computation: N+2*N*log 2 N 2016/3/107

8. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 假如 pole 只有 -j, 則 為 BPF, 但因 zero 中的 BR 影響甚大, 故此 filter 仍為 BR 1.3 Filters H 1 ( z ):LP H 2 ( z ):LP H 3 ( z ):BP H 4 ( z ):BR 2016/3/108 HPF BPF LPF BR HPF H 5 ( z ):LP H 6 ( z ):HP H 7 ( z ):BR H 8 ( z ):BR H8(z)H8(z) H4(z)H4(z)

9. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 2016/3/109 1.4 Filters Filter with real coefficient: Poles and zeros are conjugate Linear phase filter: zeros reciprocally appear Minimum phase filter: poles and zeros are all inside the unit circle (not includes unit circle) All-pass filter: poles and zeros reciprocally appear Stable filter: all of poles are inside the unit circle (not includes unit circle) (a) 1, 2, 3, 4, 6, 7, 8 (b) 3, 6 (c) None (d) 3, 4, 5, 6, 7 (e) None (f) 5, 8 15

10. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan (a) (b) Frequency transformation: Both filters of T 1 and T 2 are HPF to LPF 2016/3/1010 2.1 Filter Design Simplest transformation:

11. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan HPF to LPF 2016/3/1011 2.1 (c) Filter Design

12. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan H FIR (z) = (1+b 0 z -1 -2z -2 ) (1-3z -1 +b 1 z -2 ) (1-3z -1 +b 2 z -2 +2z -3 -b 3 z -4 +z -5 ) = (1-3z -1 +b 1 z -2 +b 0 z -1 -3b 0 z -2 +b 0 b 1 z -3 -2z -2 +6z -3 -2b 1 z -4 ) (1-3z -1 +b 2 z -2 +2z -3 -b 3 z -4 +z -5 ) = (1+(-3+b 0 ) z -1 +(b 1 -3b 0 -2)z -2 +(6+b 0 b 1 )z -3 -2b 1 z -4 ) (1-3z -1 +b 2 z -2 +2z -3 -b 3 z -4 +z -5 ) b 2 =2; b 3 =3 b 0 =6; b 1 =-0.5; 2016/3/1012 2.2 Linear Phase Filter Linear phase filter: zeros reciprocally appear ? Type I M =even, h[n]=h[M-n], 0≤n≤M Type II M =odd, h[n]=h[M-n], 0≤n≤M Type III M =even, h[n]=-h[M-n], 0≤n≤M Type IV M =odd, h[n]=-h[M-n], 0≤n≤M

13. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 2016/3/1013 H IIR (z) = =, Let K =1 2.3 All-Pass Filter All-pass filter: poles and zeros reciprocally appear

14. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan (0,0) y[2, 2] = 10 y[-1, 2]= 0 y[3, 2] = -14 y[3, 4] = 5 y[4, 2] = -5 2016/3/1014 2.4 2D - Linear Convolution y[n, m] = x[n, m] * h[n, m] = Σ k Σ l x[k, l]∙h[n-k, m-l]

15. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan (a) (b) (c) (d) 2016/3/1015 3.1 DFT

16. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan (a) (b) (c) 2016/3/1016 3.2 IDFT

17. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan 2016/3/1017 (a) (b) 3.3 N -Point DFT OROR

18. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan row column 2016/3/1018 3.4 2-D DFT OR rowcolumn (0,0)

19. MediaCore Lab, National Cheng Kung University, Tainan, Taiwan Thanks for Your Attention! 2016/3/1019