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846 Answers to Selected Problems

Section 14.6 Sampled Fourier Series
1. U 0 = 255. The other approximate values are given in Table A.12.
3. U 0 = 58.901925. The other approximate values are given in Table A.13.
5. U 0 = 31.501953. The other approximate values are given in Table A.14.

TABL E A.12 Approximate Values in Problem 1, Section 14.6

U n Approximate Value U n Approximate Value
U 1 –1 + 40.735484i U 118 –1 – 3.992224i
U 2 –1 + 20.355468i U 119 –1– 4.453202i
–1 + 13.556669i –1 – 5.027339i
U 3 U 120
–1 + 10.153170i –1 – 5.763142i
U 4 U 121
–1 - 8.107786i –1 – 6.741452i
U 5 U 122
–1 + 6.741452i –1 – 8.107786i
U 6 U 123
–1 + 5.763142i –1 – 10.153170i
U 7 U 124
–1 + 5.027339i –1 – 13.556670i
U 8 U 125
–1 + 4.453202i –1 – 20.355468i
U 9 U 126
–1 + 3.992224i –1 – 40.735484i
U 10 U 127
TABL E A.13 Approximate Values in Problem 3, Section 14.6

U n Approximate Value U n Approximate Value
U 1 –5.854287 – 32.096339i U 118 0.647851 + 2.829713i
U 2 –0.805518 – 14.788044i U 119 0.633992 + 3.157208i
U 3 0.44274 – 9.708611i U 120 0.614603 + 3.565443i
U 4 0.336014 – 7.235154i U 121 0.586989 + 4.089267i
U 5 0.470070 – 5.764387i U 122 0.542633 + 4.787014i
U 6 0.542633 – 4.787014i U 123 0.470070 + 5.764387i
0.586299 – 4.089267i 0.336014 + 7.235154i
U 7 U 124
0.614603 – 3.565443i 0.044274 + 9.708611i
U 8 U 125
0.633991 – 3.157208i –0.805518 + 14.788044i
U 9 U 126
0.647851 – 2.829712i –5.854287 + 32.096339i
U 10 U 127

TABL E A.14 Approximate Values in Problem 5, Section 14.6

U n Approximate Value U n Approximate Value
U 1 9.228787 + 17.271595i U 118 –0.400755 – 1.993017i
U 2 1.933662 + 9.790716i U 119 –0.377943 – 2.222355i
U 3 0.582715 + 6.663663i U 120 –0.346050 – 2.507623i
U 4 0.109884 + 5.028208i U 121 –0.299528 – 2.872545i
U 5 –0.108968 + 4.029124i U 122 –0.227849 – 3.356393i
U 6 –0.227849 + 3.356393i U 123 –0.108968 – 4.029124i
U 7 –0.299528 + 2.872544i U 124 0.109884 – 5.028208i
U 8 –0.346050 + 2.507623i U 125 0.582715 – 6.663663i
–0.377943 + 2.222355i 1.933662 – 9.790715i
U 9 U 126
–0.400755 + 1.993017i 9.228757 – 17.271595i
U 10 U 127

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