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College of Engineering and Information Technology Signals and Systems (ELE 204/BME 303) Tutorial MATLAB Assignment If an input to a system is given by x[n] = [7,4,1,6] and the impulse response of a system is given by h[n] = [5,4,2,8,9,3]. Find and draw the system response y[n] using MATLAB software, include the code and the generated MATLAB graph. Tutorial Assignment - Part I 1. The impulse response of a LTI system is given by h[n] = 8[n] + 8[n-1] + 8[n-3] and the input to the system is given by x[n] = 8[n] – 8[n-1]. Calculate the system response y[n] graphically. جـامـعـة عـجـمـان 2. If an input to a system is given by x[n] = [7,4,1,6] and the impulse response of a system is given by h[n] = [5,4,2,8,9,3]. Find the system response y[n] graphically using discrete time convolution. 4. The impulse response of a linear, time-invariant system is given by h(t) = {1 AJMAN UNIVERSITY 3. Consider an LTI system with the impulse response given by h(t) = u(t) — u(t-2). Determine and sketch the response of the system for the input t, x (t) = { _ t + ²₁ 0 ≤t≤1 1<t≤2 0≤t≤3 elsewhere The input x(t) applied to the system is given by x(t) Determine the response y(t) for all t. (5, 1 ≤ t ≤ 00 = (0, elsewhere
Tutorial Assignment - Part II 1. Express the following periodic signals in exponential Fourier series. a) x(t) = 2-3 cos(wot + 45°) b) x(t) = 6 + 3 cos(wot) + sin(2wot) - 5 cos(4wot) c) x(t) = cos(50лt) + 4 cos(300лt) - cos(200лt) + 7 sin(125nt) 2. Evaluate the Fourier series of the periodic square wave signal given below. -3r -2x -A w(1) 1 π 21 3r Tutorial Assignment - Part III 1. Given that x(t) → X(w), express the Fourier transform of each of the following functions using the time-shifting property. a) x(t + 7) b) x(t-3) + x(t + 5) c) x(2t - 1) 2. Given that x(t) X(w), express the Fourier transform of each of the following functions using the frequency-shifting property. a) x(t) e-j4t b) x(6t) eist 3. Determine the Fourier transform of the function x(t) = e-altl using the defining integral. 4. From the frequency-shifting property of the Fourier transform, show that if f(t) F(w), then f(t) cos(wot) → ½ [F(w + wo) + F(w + wo)].
» Tutorial Assignment - Part IV 1. For the RC circuit shown in the Figure below with R = 10 k and C = 1 μF. Determine a) The differential equation model relating the input voltage Vin(t) to the output voltage Vout(t). b) The frequency response function, H(w). c) The type of filter in this circuit. Vin a) R 2. Given the following filter H(w) = {1, ≥ 150m rad/sec |w| What is the response of the filter to x(t) = 4 cos(300лt) — cos(200¬t) + 7 sin(125лt)? b) C 3. Determine the Laplace transform of each of the following signals. a) sin(120nt) u(t) b) e 2t cos(120nt) u(t) c) 2 [u(t)- u(t-5)] d) 5 [1-e³t] u(t) e) e 2t u(t)-e-2t u(t-5) 4. Determine the inverse Laplace transform of the following. S +6 s² +9s + 20 3s + 15 s² + 25 Vout