Question #5: Consider the continuous-time signal shown below. x(t) -6 -4 -2 4 -2 (a) Sketch...
Consider the following continuous-time signal. x(t) = 1 for m < t < m + 1 −1 for m + 1 < t < m + 2 for m = − 4,−2, 0, 2, 4, · · · Sketch the following signals. (a) x(t) (b) y(t) = 2x(2t − 1) + 1
1. Use combinations of STEP FUNCTIONS to describe each continuous-time signal shown below. f(t) 0 2 4 6 0 1 2 3 0 1 2 3 4 2. Sketch the following signals: (a) x (t)=1 [u(t+2)-u(t-1)] (c) X(t)=\fety (b) X(t)=t.e (d) x (t) = u(t) u(t-1).ult-2).u(t-3) 3. Determine whether the systems below are linear and time invariant. Justify your answer! (a) y(t) = x(31) (b) y(t)= 2x(1-t) y(t)=cos(x(t)] 4. Simplify the expressions: (a) y(t)=1.8(t+2)+(t +1) 8(1-1)+(t+3). 8(t) (b) y(t) =...
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3...
Please Answer the following questions ASAP. Thanks! Transformations of independent variable 1. A discrete time signal is shown below. Sketch and carefully label x [2n 1 and xl-nlul-n1. 2. A continuous time signal x(t) is shown below. Sketch and carefully label x(t-1) and x(-t)-x(t)u(-t x(t) Even and Odd 3. Sketch x()Ev(sin(5mt)u(-t))for-1ts1 . Sketch the even and odd parts of signal x[n] in problem 1. Transformations of independent variable 1. A discrete time signal is shown below. Sketch and carefully label...
(a) The continuous-time signal x(t) with FT as depicted in the figure shown below is sampled. Sketch the FT of the sampled signal for the following sampling intervals: identify whether aliasing occurs, Ts = 1/12 X(jw) -117 107 W -10 0 117 97 97T (b) Determine the z-transform and ROC for the following time signals: x[n] = (4)"u[n] + (1)"u[ -– 1] Sketch the ROC, poles, and zeros in the z-plane.
(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...
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...
For the continuous time signal() shown in the Figure 1, sketch each of the following signals: (a) x(t-3)-3 points(b) x(2-t)-5 points(c) x(2 t+2)-5 points(d) x(2-t/3)-4 points(e) x(t)(σ(t+3/2)-σ(t-3/2))-2 points(f) (x(t)+x(2-t)) u(1-t)-6 points(g) x(t/2-3)+x(t/3-2)-6 points(h) x(t-1) u(t-1)-4 pointsσ(t) is the impulse function and u(t) is the unit step function.
Question #4: Consider the signal x(t) cos(2π (a) Sketch the signal. Please make sure to label all relevant features. (b) Is the signal continuous or discrete? Explain. (c) Is the signal even, odd, or neither? Demonstrate
Q1) For the continuous time signal below, x(t)=1+t (a) Determine the even and odd parts of the signal. (b) Sketch the signal from t = -3 to t = 3. (c) Explain why the signal does not possess BIBO stability.