Problem 3 Which of the signals below are equal to s(t)cos2T(3)t)? 0.5 0.5 0 0.5 0.5
For the remainder of this problem, the signals (t) and y(t) denote the input and output, respectively, of a stable LTI system whose (double-sided) frequency response is known to be w-4m 27T 4m H(w) = rect ( 2π with rect(t) denoting the unit-pulse function i.e., rect(t) 1 for lt| < 1/2 and is zero otherwise. Hint: Use sketches as a guide for answering each question most efficiently. (c) (15 points) Determine y(t) for all t given the applied input is...
A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally likely bits '0' and '1', respectively. The signaling duration is 4 seconds. The receiver uses a filter h(t) shown in Fig. 2 s1 (t) s2(t) 0 Figure 1: Set of signals in Problem 1 h(t) 0 Figure 2: h(t) in Problem 1 (a) Determine the parameter ri for this system. HINT: Remember that ri is equal to this convolution 81(t) * h(t) evaluated...
show all steps with explanation in clear graph: If you're not sure don't answer Problem 3 Three signals r(t), x2(t) and r3(t) are given graphically below (a) Express 2(t), r3(t) in terms of 1(t) using time shifting and amplitude scaling (No time scaling (b) If r1 (t) is applied as input to a linear time invariant system and the corresponding output is y (t) given graphically below as well, determine the outputs of the system y2(t) and y3(t) when r2(t)...
3. Let the Laplace transforms of signals (t) and y(t) be X(s) and Y(s) with appropriate regions of convergence, respectively (a) Show that the Laplace transform of x(t) * y(t) is X(s)Y (s). What is the region of convergence? (b) Show that the Laplace transform of tx(t) is -dX(s)/ds with the same region of x(t) convergence as tn-1 1 for Re{sa} > 0. -at e (c) Show that the Laplace transform of 'u(t) is n 1)! (sa)" 1 for Refsa}...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
Find the correlation between the two given signals. x(t)=sin(2pi*t) pi(t-0.5) y(t)=cos(2pi*t) pi(t-0.5) pi(t) is the unit rectangular pulse Please write legibly and explain
The periodic function so(t) with period 28 given by if 14 t<-0.5 1 if _ 0.5 〈 t < 0.5 so(t)- 0if 0.5 t< 14. has the Fourier series defined by So(0)-0.0357143 and for n 0 0.0357143 * sin(nTl/28) nT1/28 Use linearity and the shifting property to find the Fourier Series for s(t), defined by f -14 t <4.5 -5 if 4.5 t< 5.5 3 if 5.5 t<6.5 if 6.5 < t < 14. s(t) S(0) and for n S(n)...
Signals and Systems ҳL+) 0-1 3 Consider the XLt) signal, Draw the following signals in detalle N 1 G o 1 a) X(t-1) 3 2 b b) [xlt) + x(-1)] Ult) c) X(t) [S(t+Ž) -8(+-+]
7. Consider the following signals f(t) = 4e-2tu(t) _ 2e-tu(t) v(t) = 2e-t/3 sin(5t)u(t) w(t) = te-2tu(t) Which of these signals (if any) (a) has repeated poles? (b) could be the impulse response of an all pass filter? (e) has poles on the ju-axis? (d) has a DC gain of 0? (e) has a left-sided ROC (Re(s) < a)?
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0. Problem 4: Consider the following problem for the heat equation (1)...