F.T. Let r(t) and X(ju) be Fourier transform pairst)x().X(j)is shown in the figures below 2X(jo) X(jo)...
(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...
1. A signal (t) with Fourier transform X(ju) undergoes impulse-train sampling to generate where T = 4 x 10-4. For each of the following sets of constraints on r(t) and/or X(ju), does the sampling theorem guarantee that r(t) can be recovered exactly from p(t)? a. X(ju) = 0 for l니 > 1000-r b, X(ju) = 0 for lal > 5000π c. R(X(ju))-0 for lwl > 1000-r d, x(t) real and X(jw)-0 for w > 1000π e. x(t) real and X(jw)-0...
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier transform of the following signals in terms of X (jw). a. y(t) = e'*x(t – 2) b. y(t) = x(-3) c. y(t) = x(t)dt
In the previous homework, the Fourier Transform of x(t)- t[u(t)-u(t-1) was found to be x(t) 2 0 -1 -2 -3 5 4 3-2 0 2 3 4 5 a) b) Using known Fourier transforms for the terms of y(t), find Y(j). (Hint: you will have to apply some c) Apply differential properties to X(ju) to verify your answer for part b Differentiate x(t), y(t) = dx/dt. Note, the derivative should have a step function term. Include a sketch of y(t)...
Let x(t) be the signal with Fourier transform Xjw) shown below x(j) Let Xs(t) be obtained by sampling x(t) with sampling period Td let xdin]- x(nT) for all integer n. Which option is the plot of Xd(e the Fourier transform of xdinj? Instructions: First sketchXs ω which is the Fourier transtorm of xs nt is going to be infinite number of replicas of Sketch on 3 e cas. You need to n he span between heep as he )and Xole...
Problem 4 (20 points) Given that the Fourier transform of x(t) is find the Fourier transform of the following signals in terms of X(jo) a. y(t)-etx(t 1) b. y(t)-x(-t) x(t-1) c. y(t)tx(t)
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
7.21. A signal x(t) with Fourier transform X(jw) undergoes impulse-train sampling to generate where T = 10-4. For each of the following sets of constraints on x(t) and/or X(j), does the sampling theorem (see Section 7.1.1) guarantee that x(t) can be recovered exactly from xp(t)? (a) X(jo) = 0 for lal > 5000π (b) x(ja)-0 for lol > 15000m (c) Re(X(jw)} = 0 for lal > 5000m (d) x(t) real and X(ju)-0 for ω > 5000TT (e) x(t) real and...
Find the Fourier transform f(t) a. X(w-3) 8(+3) 3. 2cos3tx(t) with x(t)'s FT is X(a) 2X(w-3) + 2x(w + 3) ?(0-3) + ?(w + 3) c. d.
Find the signal x(t) whose Fourier Transform X(jω) is as follows: 0 otherwise Note that the magnitude signs around w in the definition of X(jo) mean that it is symmetric around the origin (that is, it is even). Also note that you can solve this problem using direct integration, tables, or a combination.