1. (3 marks) Show that the Fourier transform f(k) of a gaussian 5() = VZAQC with...
2 part a and b , 3 part a and b 7 marks 2. Consider the Fourier transform pair a) Use the appropriate Fourier transform properties to find the Fourier transform of te-lti 5 marks) b) Use the results from part (a) and the duality property to determine the Fourier transform of 4t f(t) = (1 +t2)2 [15 marks 3. For the discrete time system shown in fig. 1 a) Determine the transfer function Hint: The best starting point is...
5 = 10 marks ] Question 1 [3 2 (a) Use the Fourier transform, -) / Ф(Р) e'pr/h d3p 27TH and the inverse transform 1 b(FeipF/hd3r Ф(Р) 2тh to prove the Fourier Integral Theorem: 1 ') ei(F'-p)/h d3p' d*r. Ф(р) - 2тh (b) Explain why the Dirac-ô may be represented via - ih)/ 1 8(F- F') (c) Show that for arbitrary wave functions /a,b(f) that / -/ Фа (р)" фь (р) d'р, Va(r = where ba and da (and /,...
What is the Fourier transform of: Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = -28t7 Question 5 (2 marks) Attempt 1 f(t):77®е What is the Fourier transform of e-28t7 /21 Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) Skipped -28t7 Question 5 (2 marks) Attempt 1 f(t):77®е What is the Fourier transform of e-28t7 /21 Your answer should be...
Question 5 (2 marks) Attempt 1 f(t)=( Find the Fourier transform of +a)e Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w)Skipped
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
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform
Find the Fourier transform of a Gaussian function:
Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2 <Iz 5 markS ii) 2 2 (+2z Solve any three Q4A] 15 marks Is the following function even or odd? Find its Fourier series: i) 2 Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2
Please show working and explanation if possible. Thank you so much in advance b) Given that the Fourier transform of f() is g(w)- esf (7 marks) Deduce the Fourier transform of f"(t + τ). c) A Free nduction Decay (FID) signal from a certain spectroscopic experiment was measured to be 7. )- A ex exp -i2 T. for t > 0, where Q, and Ω2 are 150x106 radian/s and 200x10° radians, respectively, while T, and 7, are 25 ns and...
Find the Fourier transform of a one-dimensional rectangle function, and sketch the pair. Show how they can both be delta functions Verify that the FT of a Gaussian is a Gaussian, t2 w2 1 202 2/o2 e V2πο2 and so with o2=1, except for the constant 1//2T, ex-2 is its own Fourier transform. Show that they can both be delta functions (but not at the same time!). Sketch the transform cases for large and small variance Note there are several...