Which one of the following muscles make up the majority of t…
Questions
Which оne оf the fоllowing muscles mаke up the mаjority of the buttocks?
Questiоn 1 (5 pоints) A cоntinuous-time periodic signаl (x(t)) is reаl-vаlued and has a fundamental period [T=8.] The nonzero complex Fourier series coefficients are [a_{1}=a_{-1}=2,qquada_{3}=4j,qquada_{-3}=a_{3}^{*}=-4j.] Express (x(t)) in the form [x(t)=sum_{k}A_kcos!left(omega_k t+phi_kright),] where [omega_k=komega_0,qquadomega_0=frac{2pi}{T}.] Select the correct answer. (A) [x(t)=4cos!left(frac{pi}{4}tright)-8cos!left(frac{3pi}{4}t+frac{pi}{2}right)] (B) [x(t)=2cos!left(frac{pi}{4}tright)-4cos!left(frac{3pi}{4}t-frac{pi}{2}right)] (C) [x(t)=4cos!left(frac{pi}{4}tright)-8cos!left(frac{3pi}{4}t-frac{pi}{2}right)] (D) [x(t)=2cos!left(frac{pi}{4}tright)+8cos!left(frac{3pi}{4}t+frac{pi}{2}right)] (E) None of the above. Question 2 (5 points) Consider the discrete-time periodic signal [x[n]=1+sin!left(frac{2pi}{N}nright)+3cos!left(frac{2pi}{N}nright)+cos!left(frac{4pi}{N}n+frac{pi}{2}right),] where the fundamental period is (N). Which one of the following sets of DTFS coefficients is correct? (A) [a_0=1,qquada_{pm1}=frac{3}{2}mpfrac{j}{2},qquada_2=frac{j}{2},qquada_{-2}=-frac{j}{2},]with all remaining coefficients equal to zero. (B) [a_0=1,qquada_{pm1}=frac{3}{2}pmfrac{j}{2},qquada_2=-frac{j}{2},qquada_{-2}=frac{j}{2},]with all remaining coefficients equal to zero. (C) [a_0=0,qquada_{pm1}=3mp j,qquada_2=j,qquada_{-2}=-j,]with all remaining coefficients equal to zero. (D) [a_0=1,qquada_1=3,qquada_{-1}=1,qquada_2=frac12,qquada_{-2}=frac12,]with all remaining coefficients equal to zero. (E) None of the above. Question 3 (5 points) Determine the complex exponential Fourier series representation of the following continuous-time periodic signal: [x(t)=sin^2(t).] Select the correct answer. (A) [omega_0=2,qquada_0=frac12,qquada_{pm1}=-frac14,]with all remaining coefficients equal to zero. (B) [omega_0=1,qquada_0=frac12,qquada_{pm2}=-frac14,]with all remaining coefficients equal to zero. (C) [omega_0=2,qquada_0=frac12,qquada_{pm2}=-frac12,]with all remaining coefficients equal to zero. (D) [omega_0=1,qquada_0=1,qquada_{pm2}=-frac14,]with all remaining coefficients equal to zero. (E) None of the above. Question 4 (10 points) A periodic signal[x(t)=sum_{k=-3}^{3} a_k e^{jk2pi t}]with fundamental frequency (omega_0=2pi) is applied to an LTI system with impulse response[h(t)=e^{-t}u(t).] The nonzero Fourier series coefficients of (x(t)) are[a_0=1,qquada_1=a_{-1}=frac{1}{4},qquada_2=a_{-2}=frac{1}{2},qquada_3=a_{-3}=frac{1}{3}.] If[y(t)=sum_{k=-3}^{3} b_k e^{jk2pi t},]which of the following correctly gives the Fourier series coefficients of the output (y(t))? (A) [b_k=a_k(1+jk2pi), qquad -3le kle 3] (B) [b_k=frac{a_k}{1+jk2pi}, qquad -3le kle 3] (C) [b_k=frac{a_k}{1-jk2pi}, qquad -3le kle 3] (D) [b_k=a_k e^{-jk2pi}, qquad -3le kle 3] (E) None of the above Question 5 (15 points) Consider a continuous-time LTI system with the input-output relation [y(t)=int_{-infty}^{t} e^{-(t-tau)}x(tau),dtau.] Answer the following questions. (A) Find the impulse response (h(t)) of this system. (B) Show that the complex exponential function (e^{st}) is an eigenfunction of the system. (C) Using the impulse response obtained in part (a), determine the eigenvalue corresponding to the eigenfunction (e^{st}). Question 6 (15 points) Suppose we are given the following facts about a signal (x(t)): 1. (x(t)) is a real signal. 2. (x(t)) is periodic with period (T=4), and it has Fourier series coefficients (a_k). 3. (a_k=0) for (|k|>1). 4. The signal with Fourier series coefficients [ b_k=e^{-jkpi/2}a_{-k} ] is odd. 5. [ frac{1}{4}int_{4}|x(t)|^2,dt=frac{1}{2}. ] Determine the signal (x(t)). Question 7 (20 points) Consider a continuous-time signal (x(t)), whose CTFT is [X(jomega)=begin{cases}0.25(omega+4), & -4