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=x(t)2dtx(t)=sin2t+3cos4tE=(sin2t+3cos4t)2dtE=(sin22t)dt+(9cos24t)dt+(6sin2tcos4t)dtE=E=\int_{-\infin}^\infin\|{x(t)}\|^2dt\\ x(t)=\sin{2t}+3\cos{4t}\\ E=\int_{-\infin}^\infin({ \sin{2t}+3\cos{4t}})^2dt\\ E=\int_{-\infin}^\infin({ \sin^2{2t})dt+\int_{-\infin}^\infin( 9\cos^2{4t}})dt+\int_{-\infin}^\infin(6\sin{2t}\cos{4t})dt\\ E=\infin

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

x(t)=sin2t+3cos4tx1(t)=sin2tω1=2T1=2πω1T1=2π2=πx2(t)=3cos4tω2=4T2=2πω2T2=2π4=π2x(t)=\sin{2t}+3\cos{4t}\\ x_1(t)=\sin{2t}\\ \omega_1=2\\ T_1=\dfrac{2\pi}{\omega_1}\\ T_1=\dfrac{2\pi}{2}=\pi\\ x_2(t)=3\cos{4t}\\ \omega_2=4\\ T_2=\dfrac{2\pi}{\omega_2}\\ T_2=\dfrac{2\pi}{4}=\dfrac{\pi}{2}\\

To=T1=2T2=1T_o=T_1=2T_2=1\\

P=1To0Tox(t)2dtP=1101sin2t+3cos4t2dtP=01sin22tdt+901cos22tdt+601sin2tcos3tdt=5sin4=4.93JP=\dfrac{1}{T_o}\int_0^{T_o}\|{x(t)}\|^2dt\\ P=\dfrac{1}{1}\int_0^{1}\|{\sin{2t}+3\cos{4t}}\|^2dt\\ P=\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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