Chapter 18-Electrical Circuit Analysis-Problem Solutions, Exercises of Electrical Circuit Analysis

Download Chapter 18-Electrical Circuit Analysis-Problem Solutions and more Exercises Electrical Circuit Analysis in PDF only on Docsity! Chapter 18, Problem 1. Obtain the Fourier transform of the function in Fig. 18.26. Figure 18.26 For Prob. 18.1. Chapter 18, Solution 1. )2t()1t()1t()2t()t('f −δ+−δ−+δ−+δ= 2jjj2j eeee)(Fj ω−ω−ωω +−−=ωω ω−ω= cos22cos2 F(ω) = ω ω−ω j ]cos2[cos2 docsity.com Chapter 18, Problem 2. Figure 18.27 For Prob. 18.2. Chapter 18, Solution 2. ⎢ ⎣ ⎡ << = otherwise,0 1t0,t )t(f f"(t) = δ(t) - δ(t - 1) - δ'(t - 1) Taking the Fourier transform gives -ω2F(ω) = 1 - e-jω - jωe-jω F(ω) = 2 j 1e)j1( ω −ω+ ω or ∫ ω−=ω 1 0 tj dtet)(F But ∫ +−= c)1ax(a edxex 2 ax ax ( ) =−ω− ω− =ω ω− 1 02 j )1tj( j e)(F ( )[ ]1ej11 j2 −ω+ω ω− t f ‘(t) 1 0 -δ(t-1) 1 t f ”(t) δ(t) -δ(t-1) –δ’(t-1) docsity.com −δ′−−δ−δ++δ′++δ−=′′ ω−ω−ωω )1sin(cos4)(G 2 −ωω+ωω =ω t 0 2 g’ –2 –1 2δ(t+1) –2δ(t–1) 1 t 0 4δ(t) g” –2 –1 2δ’(t+1) –2δ(t–1) 1 –2δ(t+1) –2δ’(t–1) docsity.com Chapter 18, Problem 5. Obtain the Fourier transform of the signal shown in Fig. 18.30. docsity.com