(b) Based on Figure Q3(b), give the expression for signal x(t) in unit step function. From...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
Name 2. (10 points) a) Find an expression for the Fourier Transform of the signal use the tables provided. illutrated below- you may 1.5p 0.5 05 2 1.5 1 0.5 0 0.51 1.5 2 b) Using your result from part (a), find an expression for the Fourier Transform of the signal c) Using your result from part (a), find an expression for the Fourier Transform of the signal d) Note that the signal p(o) illustrated below can be expressed as...
Figure 1 [Rajah I (8 MarksMarkak) (b) Evaluate the signal in Figure 2 and create the expression of Fourier coefficient to filter the signal by its k-th harmonic. State the characteristic of the obtained signals Nlaikan isyarat dalam Rajah 2 am hasilkon nekapan pekali Fowrier twk menapis isyarat melalui harmowik ke-k. Nyatakan ciri-ciri ixyrar ng dihasilkan.J x [n Figure 2 Rajah 2 (12 Marks Markak) (c) Use the definition of Continuous Time Fourier Transform (CTFT) to determine the frequency domain...
c) For the circuit shown in Figure 3, where u(t) is the unit step function, using Laplace transform methods and showing all working, find the response i(t) fort> 0. (9 marks) 4H 7e-u(t) v(1) 352 322 Figure 3
e2"u(-?) where u(9) is the usual CT unit step. 3. what signal x(t) has Fourier Transform X(ja) (10 pts.)
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
(b) Figure Q3(b) show the unit step responscs of a system A and system B, respectively For each system Find the percentage overshoot, % OS and the Peak time, T 6 marks Find the transfer function of both systems (i) [8 marks iii) You have to design a system which operate with settling time less than 5second, overshoot percentage less than 30% and which system will you choose, system A or system B, justified your answer. [3 marks |(ii) 1,5-...
1 if t>0 Consider the unit step function u(t) if t0 0 if t< The Fourier transform of the unit step function is: U(ω)-Flu (t)]- πδ(w) + 1 , and the graph of the unit step function is shown below: u(t) 1/2 Relate intuitively each term of the Fourier transform U() given above to the corresponding parts f you find it helpful). Explain briefly below. 1 if t>0 Consider the unit step function u(t) if t0 0 if t
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T, x) T T1 Find the Fourier transform of the signal and sketch it