6 This assignment is used to clarify the difference between Ch3 (Fourier Series) and Ch4 (Continuous-Time Fourier Transform). 1. Let ( t, 0t1 x(t) = 2 t, 1 t 2 be a periodic signal with fundamental period T = 2 and Fourier coefficients ak . (a) determine the value of a0 . (b) determine the Fourier series representations of dx(t)/dt. 2. Determine the Fourier series coefficients for each of the following discrete-time periodic signals: (a) x[n] periodic with period 4 and x[n] = sin n 4 for, 0 n 3 n 4 for, 0 n 15 (b) x[n] periodic with period 16 and x[n] = sin 3. For a LTI system with impulse response h(t) = e2t u(t). If the input (a) x(t) = cos(3t), what is the output y(t)? (b) x(t) = e(j(3t+/4)) , what is the output y(t)? (c) x(t) = e(3t) u(t), what is the output y(t)? 4. For a causal LTI system with frequency response H(jw) = 1 jw + 3 (a) If the input x(t) = e4t u(t), what is the output y(t)? (b) If the input x(t) = cos(4t), what is the output y(t)? 1