04. (25 pts)(Fourier Analysis) A periodically driven oscillator and the forcing function is shown tbelow. F(t) The gove...
2. Solve for the motion of a driven-damped harmonic oscillator whose forcing function F(t) is given by F(t) = 0, < 0 HU t 12 0 <t<T PO) – 4(), 0<t<7 F(t) = A, t>t. m т.
The Fourier Transform of a certain time function, x(t), is shown below F{x(t) x(f) 2.5 7 1.5 1 0.5 -30 -20 -10 10 20 30 f(Hz) equation for X(f A. Write an B. Write an equation for x(t). C. Write and equation for the Fourier Transform of x(2t) and draw a sketch D. Write and equation for the Fourier Transform of x(t) and draw a sketch equation for the Fourier Transform of x()cos(2 E. Write an 15 t and draw...
Condsider the ODE d2 x () + 32 x (t) = F (t) where the forcing function is given by the Fourier series with co -1, c18, Assuming a particular solution of the form find and enter the exact values of an and bn requested below Cn cos (n t), 3p (t)-a0 + Σο.1 (an cos (n ) + bn sin (n t))
Condsider the ODE d2 x () + 32 x (t) = F (t) where the forcing function...
(b) The signal f(t) is shown in the figure below 3 2 f(t) _ 0 I 1 -4 -3 -2 -1 0 1 2 3 4 5 6 7 t and is given by 21 (1) + 3A (132), where A is the triangle function defined as 10-{ It a It <a It > a 0 Write the Fourier transform F [A(t)] (s) of f(t) exploiting the fact that FA(t)](s) = sinc-(s) where sin(TTS) sinc(s) ITS and the theorem for...
Question Question 5 (2 marks) Attempt 1 Find the Fourier transform of: f(t) ˊ-e-10t Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = π(164t2)2
Question Question 5 (2 marks) Attempt 1 Find the Fourier transform of: f(t) ˊ-e-10t Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = π(164t2)2
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2.1, determine both the DC coefficient ao and a general expression for the other Fourier series coefficients ak. Do this by hand, not in Matlab. Show all your work in your lab report. You can add these pages as hand-written pages, rather than typing them in to your lab report, if you prefer Hint 1: It will be easiest to integrate this function from...
29.9) Compute the Fourier transform of the periodic function
f(t) to prove the equation shown below:
29.9. Let f(t) = iftl > T. 0 Show that f(w) =
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...
(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 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