Ssp 2013 Problems(Pfiev)

8/13/2019 Ssp 2013 Problems(Pfiev)

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12/12/2013

AssignmentStochastic Signal Processing

(Solving below problems using values given in Table 1)

Problem 1: Spectral estimation

Consider a sum of sinusoids in white Gaussian noise. The sinusoids are with frequencies

of fs, fs and fs, and with amplitudes of a, b and c, respectively. The fs is samplingfrequency. Number of signal samples is d, DFT size is e. The white Gaussian noise iswith variance of 1 and zero mean. Plot the estimated spectrum of sum of sinusoids in

white Gaussian noise usingf.

Problem 2: LCMV beamforming

There uncorrelated zero-mean narrowband signals located in far-field are impinging at a

uniform linear array with three antenna elements. The antenna elements are omni-

directional. The relative distance between two antennas is / = 0.5, where is the

wavelength of the signals. The directions of arrival are 1 = A, 2 = B, 3 = C. The

signals are with the receiving powers P1 =1, P2 = 1 and P3 = 1.

a) Determine the array steering vectorsa(i) (i =1, 2, 3) for three signals above.

b) Calculate the correlation matrixRiof three signals above(i =1, 2, 3).

c) Calculate the total receive correlation matrixR.

d) Which condition must the beamforming vectorw= [w1, w2, w3]T fulfill to provide an

array gain of one in the direction = A, where the array gain is defined bywHa().

e) Calculate the beamforming vectorw that minimizes the output powerwHRw by

taking the constraint of question d) into account.

f) Calculate the beamforming vectors that minimize the output power, while

providing simultaneously array gain of one in the directions of = A and = B.


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12/12/2013

Table 1

Group a b c d e f A B C D

1 0.15 0.40 0.35 1 5 4 80 2048 P, BT 30 0 -30 10

2 0.40 0.10 0.35 5 1 5 80 1024 P, BT 10 0 -10 12

3 0.25 0.20 0.05 4 5 1 60 2048 M, BT 30 0 -20 9

4 0.35 0.15 0.30 4 3 5 60 1024 M, BT 10 30 -10 9

5 0.35 0.25 0.40 5 1 5 240 1024 B,W 30 5 -30 11

6 0.30 0.10 0.20 1 5 1 80 1024 B, BT 50 0 -40 10

7 0.25 0.35 0.45 5 3 3 80 1024 B, W 10 -5 -20 11

8 0.37 0.15 0.34 4 1 5 240 2048 B, BT 5 0 -5 12

9 0.40 0.20 0.35 5 1 5 240 1024 B,W 40 10 -20 10

10 0.30 0.25 0.33 5 2 5 240 2048 B, W 25 0 -25 12

11 0.10 0.15 0.30 3 3 5 120 2048 P, W -10 -20 -30 11

12 0.17 0.20 0.35 5 5 1 240 2048 P, W 35 5 -30 10

13 0.35 0.15 0.18 2 5 5 240 2048 M, BT 40 0 -40 9

14 0.40 0.10 0.30 1 5 5 60 2048 P, B 15 -5 -25 11

15 0.15 0.45 0.25 1 5 1 120 1024 B, M 15 5 -5 12

16 0.10 0.25 0.20 1 5 1 120 1024 W, BT 30 0 -30 11

17 0.20 0.30 0.25 1 5 5 80 2048 W, BT 25 5 -10 10

18 0.30 0.40 0.26 5 1 5 120 2048 P, BT 10 -10 -40 9

19 0.35 0.20 0.16 1 5 5 240 2048 M, W 15 30 -5 12

20 0.25 0.15 0.11 3 5 5 120 1024 P, W 40 5 -25 10

21 0.10 0.35 0.38 1 4 5 120 2048 P, BT 10 0 -15 9

22 0.15 0.40 0.12 5 1 5 240 2048 B, BT 20 -5 -25 10

23 0.27 0.35 0.20 5 5 1 80 1024 P, W 15 5 -25 12

24 0.40 0.35 0.10 4 5 2 80 2048 M, W 35 0 -25 9


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1/5/2014 19:58:55 60901225 Hong V Xun Khoa 40902364 on Nht Tn 11/5/2014 20:05:56 50901136 Phan Thanh Hng 50901152 V Anh Kha 21/5/2014 20:25:31 P0910006 Huyfnh Minh Thuyt P0910004 Vn Ph Nguyn 31/5/2014 20:28:21 40902371 Lu Hong Tn 40903123 Phm Hong Tun 4

1/5/2014 20:40:07 40902635 Phm Ngc Thoan 40900797 Lm Thanh Hiu 51/5/2014 21:05:48 20800058 Nguyn Quc Anh 40901556 Ng Hong Nht Minh 61/6/2014 22:04:54 40903113 Nguyen Oanh Tuan 40902947 Le Thuc Trinh 71/6/2014 22:54:28 50900152 V Thch Bo 20900328 V Quc Cng 8

80902940 Trng Hong Tr 40800936 Nguyn Khnh 940901817 Nguyn Vn Nhn 10

Timestamp

MSSV 1

Tn SV 1

MSSV 2

Tn SV 2

ti


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Cc ti Bi tplnmn Xl nh(2013)ti 1: Dng phngphp lctrung bnh v lctrung bnh thchnghi cithinchtlngnhkhi nhgcbnhiuGauss.

a). Chn2 nh: mtnht chi titv mtnhnhiuchi tit, tonhiuGauss cho 2 nhtrn. Vitchngtrnh m tcc phngphp lc trn. Hinthcc nhsau khi xl.

b).nhgi hiuquca2 blctrn thng qua thng sRMSE(gianhbnhiuv nhsau khi xl) vinhiumcnhiuGauss khc nhau. Nhnxt.

ti 2: Dng phngphp lcmedian v lcmedian thch nghicithinchtlngnhkhi nhgcbnhiumuitiu.

a). Chn2 nh: mtnht chi titv mtnhnhiuchi tit, to

nhiumuitiu cho 2 nhtrn. Vitchngtrnh m tcc phngphp lc trn. Hinthcc nhsau khi xl.

b).nhgi hiuquca2 blctrn thng qua thng sRMSE(gianhbnhiuv nhsau khi xl) vinhiumcnhiumuitiu khc nhau. Nhnxt.


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ti 3: Gisnhbi nhe do chuynngtheo phngxv yvitcdchchuyntheo phngxv yl x0(t) = y0(t) = 0.1t /TviT = 1.

Xc nhhm lm nhe nh. Chn2 nh: mtnht chi titvmtnhnhiuchi tit, lm nho 2 nhtrn bnghm gy nhocho.

Vitchngtrnh khi phccc nhnhe trn dng blcWiener trong 2 trnghp: c v khng c nhiuGauss cng

vo.

ti 4: Vitchngtrnh nn/giinn nhkhng tnhao datrngiithutHuffman. Lyv dvinhiunhkhc nhau (nht chi titv nhnhiuchi tit). Xc nhtsnn cacc nhv dtrn.

ti 5: Vitchngtrnh nn/giinn nhc tnhao datrnchunJPEG. Lyv dvinhiunhkhc nhau (nht chi titvnhnhiuchi tit). Xc nhtsnn cacc nhv dtrn.


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ti 6: Vitchngtrnh nn/giinn nhkhng tnhao datrngiithutnn tin(LZW). Lyv dvinhiunhkhc nhau (nht chi titv nhnhiuchi tit). Xc nhtsnn cacc nhv d

trn.

ti 7: Vitchngtrnh thchinnhndngngthngtrongmtnhcho trcbngbiniHough. Minh hoktquvinhiuv dkhc nhau.

Lu: Mtnhm tia3 sinh vin. Minhm chn1 trong snhngti trn thchin. Cc ktqusao chp skhng c

tnh im. Giktqubao gmhnh nh/sliuv code (MatlabhocC) vachemail: [email protected]/01/2014).
mailto:[email protected]:[email protected]


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1/5/2014 19:59:27 40902364 on Nht Tn 60901225 Hong V Xun Khoa 1

1/6/2014 11:11:28 50901136Phan ThanhHng 50901152 V Anh Kha 80902940 Trng Hong Tr 2

1/6/2014 11:26:06 P0910006

Hunh Minh

Thuyt P0910004 Vn Ph Nguyn 31/6/2014 11:27:42 40902371 Lu Hong Tn 40903123 Phm Hong Tun 40901817 Nguyn Vn Nhn 41/6/2014 21:32:08 40900797 Lm Thanh Hiu 40902635 Phm Ngc Thoan 20800058 Nguyn Quc Anh 51/6/2014 22:55:30 50900152 V Thch Bo 20900328 V Quc Cng 40800936 Nguyn Khnh 6

1/6/2014 23:00:29 40903113Nguyen OanhTuan 40902947 Le Thuc Trinh 40901556 Ngo Hoang Nhat Minh 7

Timestamp MSSV 1 Tn SV1 MSSV 2 Tn SV 2 MSSV 3 Tn SV 3 ti

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Ssp 2013 Problems(Pfiev)