answer a and b only Suppose that two continuous time signal are given by x(t) and...
(b) Consider continuous-time signals xi(t) and x2(t) respectively given as (t +1 -1 <t<o x1(t) = { 2 Ost<2 , I 0 otherwise x2(t) = u(t) – uſt – 2). Find the convolution xı(t) * x2(t). (15 marks)
(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...
I need a Matlab code example plz
1. Suppose x(t) -3u(t+3) - u(t)+ 3H(t-3) - 5H(t-6) a. Sketch x(t). b. For the signal x(t) given, determine and sketch the following signals: ,g(t) x(t-6) g2(t) - x(3t-6) ii. s(t) x(3t-6) +2 c. Create a MATLAB script that uses a function to express x(t), and plots x(t) in the time interval- 5 < t < 8s, using a time increment of At= 0.01s. Next, use the function to graph each of the...
Find the convolution of the following two signals: X(t) ylt). Plot the resulting signal. 1. 0 x (t) y (t)
(1) Consider the following continuous-time signal: (1) 2ua(-t+t)ua(t), where its energy is 20 milli Joules (2 x 103Joules). The signal ra(t) is sampled at a rate of 500 samples/sec to yield its discrete-time counter part (n) (a) Find ti, and hence sketch ra(t). (b) From part (a), plot r(n) and finds its energy (c) Derive an expression for the Fourier transform of a(n), namely X(ew). (d) Plot the magnitude spectrum (1X(e)) and phase spectrum 2(X(e). (e) Consider the signal y(n)...
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...
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...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is sampled at t = 0.01 n to get a the discrete-time signal x[n], which is then applied to an ideal DAC to obtain a reconstructed continuous time signal y(t). a. i. Determine x[n] and graph its samples, using Matlab, along with the signal x(t) in one plot, plot a few cycles of x(t). ii. Determine the reconstructed signal,...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...