Answer to Question #226175 in Electrical Engineering for Jahangir alam

Question #226175

Classify the following signal as energy signal or power signal. Find the

normalized energy or normalized power.

(i) sin 2t + 3 cos 4t


1
Expert's answer
2021-08-17T08:35:02-0400

"E=\\int_{-\\infin}^\\infin\\|{x(t)}\\|^2dt\\\\\nx(t)=\\sin{2t}+3\\cos{4t}\\\\\nE=\\int_{-\\infin}^\\infin({ \\sin{2t}+3\\cos{4t}})^2dt\\\\\nE=\\int_{-\\infin}^\\infin({ \\sin^2{2t})dt+\\int_{-\\infin}^\\infin( 9\\cos^2{4t}})dt+\\int_{-\\infin}^\\infin(6\\sin{2t}\\cos{4t})dt\\\\\nE=\\infin"

Signal has infinite energy so it's not an energy signal

"x(t)=\\sin{2t}+3\\cos{4t}\\\\\nx_1(t)=\\sin{2t}\\\\\n\\omega_1=2\\\\\nT_1=\\dfrac{2\\pi}{\\omega_1}\\\\\nT_1=\\dfrac{2\\pi}{2}=\\pi\\\\\nx_2(t)=3\\cos{4t}\\\\\n\\omega_2=4\\\\\nT_2=\\dfrac{2\\pi}{\\omega_2}\\\\\nT_2=\\dfrac{2\\pi}{4}=\\dfrac{\\pi}{2}\\\\"

"T_o=T_1=2T_2=1\\\\"

"P=\\dfrac{1}{T_o}\\int_0^{T_o}\\|{x(t)}\\|^2dt\\\\\nP=\\dfrac{1}{1}\\int_0^{1}\\|{\\sin{2t}+3\\cos{4t}}\\|^2dt\\\\\nP=\\int_0^{1}\\sin^2{2t}dt+9\\int_0^{1}\\cos^2{2t}dt+6\\int_0^{1}\\sin{2t}\\cos{3t}dt=5-\\sin4=4.93J"

signal is a power signal


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