T-61.3010 Digitaalinen signaalinkäsittely ja suodatus T-61.3010 Digital Signal Processing and Filtering ============================================================ RATKAISUJA / SOLUTIONS PART 6 ============================================================ ------------------------------------------------------------ (33) 1. välikoe / 1st mid term exam, 6.3.2010 ------------------------------------------------------------ Monivalintatehtävä 1:n yhteispisteet Multichoice Problem 1 Kohdittain / Statement by statement: kok.lkm / total count N=26: väite: [oikea(t)] lkm[A/B/C/D/-/Z] [vastaus%]:[A/B/C/D/Z]%:/ok%/ statem.: [correct] count[A/B/C/D/-/Z] [reply%]:[A/B/C/D/Z]%:/ok%/ 1.1: [C] [1/0/24/1/0/0] [100%]:[4/0/92/4/0]% :/92%/ 1.2: [D] [0/1/1/23/1/0] [96%] :[0/4/4/92/0]% :/88%/ 1.3: [B] [4/21/0/1/0/0] [100%]:[15/81/0/4/0]% :/81%/ 1.4: [BD] [1/12/0/9/4/0] [85%] :[5/55/0/41/0]% :/81%/ 1.5: [BCD] [2/5/1/16/2/0] [92%] :[8/21/4/67/0]% :/85%/ 1.6: [D] [2/1/1/20/2/0] [92%] :[8/4/4/83/0]% :/77%/ 1.7: [B] [1/18/0/4/3/0] [88%] :[4/78/0/17/0]% :/69%/ 1.8: [C] [0/0/21/0/5/0] [81%] :[0/0/100/0/0]% :/81%/ 1.9: [A] [14/5/2/3/2/0] [92%] :[58/21/8/12/0]%:/54%/ 1.10:[D] [0/6/3/4/13/0] [50%] :[0/46/23/31/0]%:/15%/ 1.3: (A) parallel h_1+h_2, (B) series/cascade h_1(*)h_2 1.5: (A) feedback?, (B) only certain diagram blocks, (C) stability *must* be checked, stable in *this case* 1.9: (A) zeros symmetrically, (B) z^8+1=0, e.g. if z=j: (j^2)^4+1 = (-1)^4+1 = 2 != 0 (C) h[n] = d[n] + d[n-8], (D) H(e^jw) = e^-j4w [ + ] 1.10: (B) convolution as a sum of scaled and shifted "kiisseli". Now a shift of max 9 samples, 9/22050 s, voice 330m/s, ... Pistekeskiarvo / Mean: N=26: 7.2 p / 9 p. Datahistogrammi kokonaispisteistä nähtävillä / Histogram of total points: http://www.cis.hut.fi/Opinnot/T-61.3010/VK1_K2010/monivalinta_vk1A_k2010.png Tehtävä 2 / Problem 2 Second order stable IIR highpass filter H(z) = 1/[1 + 1.4 z^-1 + 0.48 z^-2] Show some views as in MTE1-homework Problem #3 or [P55] ------------------------------------------------------------ (34) 1. välikoe / 1st mid term exam, 12.3.2010 ------------------------------------------------------------ Monivalintatehtävä 1 Multichoice Problem 1 Kohdittain / Statement by statement: kok.lkm / total count N=63: väite: [oikea(t)] --> lkm[A/B/C/D/-/Z] [vastaus%]:[A/B/C/D/Z]%:/ok%/ statem.: [correct] --> count[A/B/C/D/-/Z] [reply%]:[A/B/C/D/Z]%:/ok%/ 1.1: [C] [0/1/56/6/0/0] [100%]:[0/2/89/10/0]% :/89%/ 1.2: [A] [58/3/2/0/0/0] [100%]:[92/5/3/0/0]% :/92%/ 1.3: [A] [33/20/4/1/5/0] [92%] :[57/34/7/2/0]% :/52%/ 1.4: [ABC] [26/1/12/14/10/0] [84%] :[49/2/23/26/0]%:/62%/ 1.5: [B] [2/41/2/12/6/0] [90%] :[4/72/4/21/0]% :/65%/ 1.6: [D] [5/11/4/34/9/0] [86%] :[9/20/7/63/0]% :/54%/ 1.7: [D] [8/2/10/28/15/0] [76%] :[17/4/21/58/0]%:/44%/ 1.8: [A] [42/2/0/0/19/0] [70%] :[95/5/0/0/0]% :/67%/ 1.9: [C] [3/9/23/4/24/0] [62%] :[8/23/59/10/0]%:/37%/ 1.10:[C] [10/0/39/2/12/0] [81%] :[20/0/76/4/0]% :/62%/ Muutamia kommentteja / Some comment: 1.3: (A) parallel h = h_1+h_2, (B) series/cascade h = h_1(*)h_2 1.4: Matlab #2 (R03), problem 3: H(z) = 0.5 (1 + z^-1), 1st order linear-phase FIR 1.5: (D) The longer period T_i, the lower frequency f_i << f_T/2, no aliasing 1.6: Poles at imaginary axis are close to the unit circle => max at omega=pi/2; no zeros, only four poles "symmetrically" 1.7: H(z) = 4/[1 + 0.8z^(-1)] - 3/[1 + 0.6z^(-1)] = ... = 1/[1 + 1.4 z^(-1) + 0.48 z^(-2)] Poles at -0.6 and -0.8 1.8: Fourier transform is a linear operation 1.9: e^(j omega_k n) x[n] <-> X(e^j(omega - omega_k)) Now a shift of omega_k = pi, e^(j pi n) = (-1)^n Pistekeskiarvo / Mean: N=63: 5.8 p / 9 p. Datahistogrammi kokonaispisteistä nähtävillä / Histogram of total points: http://www.cis.hut.fi/Opinnot/T-61.3010/VK1_K2010/monivalinta_vk1B_k2010.png Tehtävä 2 / Problem 2 Second order causal and stable IIR lowpass filter H(z) = [2 - 0.4 z^-1 + 0.04 z^-2]/[1 - 0.6 z^-1 - 0.16 z^-2] Poles at -.2 and .8, zeros at .1+-.1 Show some views as in MTE1-homework Problem #3 or [P55]