hw6 - HOMEWORK 6 ECE 220 Due May 3, 2005 1. Use Fourier...

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Unformatted text preview: HOMEWORK 6 ECE 220 Due May 3, 2005 1. Use Fourier transform pairs to find x(t) in each of the following cases. (a) X(j) = (c) X(j) = 2j -j0.4 . 0.3+j e (b) X(j) = 3 - 2 cos . 1 2+j - 1 5+j (d) X(j) = j( - 17) - j( + 17). CD: "Inverse Fourier Transforms" 2. Find the Fourier transform H(j) of h(t) = Also, plot |H(j)| versus . CD:"Forward Fourier Transforms" 3. Find the inverse Fourier transform of X(j) = 2 4 - (2 + j)2 1 - j d dt sin(6(t - 2)) (t - 2) (Hint: It might help to rewrite the first term as a product.) 4. Let x(t) be a triangular pulse defined by x(t) = 2 - 2|t| |t| < 2 0 elsewhere (a) By taking the derivative of x(t), use the derivative property to find the Fourier transform of x(t). (b) Now find the Fourier transform of x(t) by differentiating x(t) twice and using the differentiation property (with order 2). Compare your results with those from (a). 5. Problem 11.12 from your text. 6. Problem 12.4 from your text. 7. Problem 12.6 from your text. 8. Problem 12.12 from your text. 9. CHALLENGE PROBLEM: 12.14 (a) and (b) from your text. ...
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