Page 865 - Advanced_Engineering_Mathematics o'neil

Answers to Selected Problems 845

TABLE A.9 Approximate Discrete Fourier Transform Values in Problem 5,
Section 14.5
k D[u](k)

–4 –14.00000 + 10.39230i
−7
–3 –15.00000 + 0.22023(10 )i
–2 –14.00000 – 10.39230i
–1 –6.00000 – 31.17691i
0 55.00000
1 –6.00000 + 31.17691i
2 –14.00000 + 10.39230i
−7
3 –15.00000 – 0.22023(10 )i
4 –14.00000 – 10.39230i

TABL E A.10 Approximate Values in Problem 13, Section 14.5
k Complex Coefficients d k DFT Approximations f k

–3 –0.005177 + 0.075984i 0.000346 + 0.075849i
–2 0.011816 + 0.115622i –0.006293 + 0.115532i
–1 –0.051259 + 0.250780i –0.045737 + 0.250753i
0 0.454649 0.460171
1 –0.051259 – 0.250798i –0.045737 – 0.250753i
2 –0.011816 – 0.115622i –0.006293 – 0.075849i
3 –0.005177 – 0.075984i 0.000346 – 0.075849i

TABL E A.11 Approximate Values in Problem 15, Section 14.5

k Complex Coefficients d k DFT Approximations f k
–3 0.005629 – 0.053051i 0.001733 – 0.052956i
–2 0.012665 – 0.079577i 0.008769 – 0.079514i
–1 0.050661 – 0.159155i 0.046765 – 0.159123i
0 0.33333 0.329437
1 0.050661 + 0.159155i 0.046765 + 0.159123i
2 0.012665 + 0.179577i 0.008769 + 0.079514i
3 0/005629 + 0.053052i 0.001733 + 0.052956i

6 −ik 2πijk/7
1
9. u j = e e
7 k=0
u 0 = 0.103479 + 0.014751i,u 1 = 0.933313 − 0.296094,
u 2 =−0.094163 + 0.088785i,u 3 =−0.023947 + 0.062482i,
u 4 = 0.004307 + 0.051899i,u 5 = 0.025788 + 0.043852i,
u 5 = 0.051222 + 0.034325i
1 4 2πijk/5
11. u j = co(k)e
5 k=0
u 0 = 1.096542,u 1 =−0.249644 − 0.232302i,u 2 =−0.201697 − 0.084840i
u 3 =−0.193858,u 4 =−0.201697 + 0.084840i,u 5 =−0.249644 + 0.232302i

13. Approximate values are given in Table A.10.
15. Approximate values are given in Table A.11.

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October 14, 2010 17:50 THM/NEIL Page-845 27410_25_Ans_p801-866