Rectangular Waves and the Sampling Function question:
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Rectangular Waves and the Sampling Function question: 2.1 Compute and sketch the time domain and (two-sided)...
Write the time domain function r(t) of the graph below as the sum of two rectangular pulse functions, then compute the fourier transform X(w) in terms of sinc function. (Reminder: A rectangular pulse centered 50,427 at the origin with width 27 is defined as II(t) = 11, -T<t<+T and it has the fourier transform II(t) sincwr)) 1 0 Amplitude -1 -2 0 2 3 8 9 10 11 5 6 7 Time-
Write the time domain function z(t) of the graph below as the sum of two rectangular pulse functions, then compute the fourier transform X(w) in terms of sinc function. (Reminder: A rectangular pulse centered fo.lt21 at the origin with width 27 is defined as II(t) = 11.-T <t< + and it has the fourier transform II(t) sinc(wr)) 3 2 Amplitude 0 0 1 2 3 4 5 6 7 8 9 10 11 Time
Problem 3: Sampling a Cosine (again) The continuous-time signal ra(t) = cos (150) is sampled with sampling period T, to obtain a discrete-time signal x[n] = XanT). 1. Compute and sketch the magnitude of the continuous-time Fourier transform of ra(t) and the discrete-time Fourier Transform of x[n] for T, = 1 ms and T, = 2 ms. 2. What is the maximum sampling period Ts max such that no aliasing occurs in the sampling process?
Question 11 pts x(t) is a time domain function. The laplace transform of x(t) is in what domain: s domain none of the above f domain time domain Flag this Question Question 21 pts if X(s) is the Laplace transform of x(t), then 's' is a : real number integer complex number rational number Flag this Question Question 31 pts In a unilateral Laplace transform the integral, the start time is just after origin (0+) just before origin (0-) origin...
1. A certain function of time x (t) has the Fourier transform X(f) shown below Sketch the spectrum of [x(t)]2 and find its bandwidth. Sketch the spectrum of [x(t)cos(2r15t)] and find its bandwidth. a. b. 11 -10 9 9 10 11
Question 2: (26 marks) 2.1 Find the The Laplace transform of the following function t, if 03t<1 2t, if t1 [3] 2.2 Find the inverse Laplace transform of 10e 2 52 - 53 +632 - 25 + 5 (10] 2.3 Find y(4) if y(t) = u(t){t - 2)2 - us(t)/(t - 3) - 2) - us(t)e' (51 2.4 Solve the following initial value problem given by y" + 4y = 28.(t) (0)=1/(0) = 0 181 Question 3: (17 marks) Let...
thx!!!! Question 3 (5.5 marks) a) Find the transfer function of the electrical circuit shown in Figure 1. What is the value of the steady state gain(s), if any? b) If R1 1, R2 = 2n, C\ = 2- 10-3F, C 1-10-3F, calculate the time constants of the system (if any). c) Find the initial and final values of the unit impulse response of the circuit d) Derive the time-domain expression of the output if the input is the function...
Clear steps, please. Question # 4(a) a. Time period of x(t) Cos(10Tmt) issec b. Time period of x(t) Cos(10Tt) +Cos (50Tt) issec c. Frequency of x(t) Cos(10mt) isHz d. Frequency ofx(t) Cos(10mt) + Cos(50πt) is- --Hz e. Phase spectrum is anfunction of frequency. f. Magnitude spectrum is an g To check stability in time domain, a system H(s) is stable if and only if function of frequency. h. To check stability in time domain, a system ht) is stable if...
TEE301/05 Question 3 (20 marks) An RLC circuit with a 1V DC source is shown in Fig. 1: i(t) Vout - R-0.22 L-0.1 H C- 10 F Fig. 1 (a) List two properties of Laplace transform. Explain these two properties. [6 marks] (b) Assume that the initial inductor current is OA and initial capacitor voltage is 0.4 V 4 marks] (c) Determine the current, t) in time domain by performing inverse Laplace transform. [4 marks) determine the expression of the...
Question 1: Compute graphically the convolution, f(t) fit) f2(t), of the following two time-functions (t) and f2(t). Sketch your final result f(t)· (Hint: To avoid having to do twice as many calculations, you may want to use these properties of convolution: the distributive and the shift properties.) fi(t) f2(t) +3 +4 +5 -1 0 +1 t -1 0