Problem 1 [8 points] (Fourier transform) Compute the Fourier transforms of the following signals. In the following, u(t)

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Problem 1 8 Points Fourier Transform Compute The Fourier Transforms Of The Following Signals In The Following U T 1 (56.9 KiB) Viewed 19 times

Problem 1 [8 points] (Fourier transform) Compute the Fourier transforms of the following signals. In the following, u(t) denotes the unit step function and the symbol * denotes convolution. i) [1 point] r(t) = e-3|t| ii) [2 points] x(t) = te-3|t|. iii) * [2 points] r(t) = e-3t cos(7t)u(t). iv) * [3 points] Consider a linear time-invariant system with output y(t) = x(t) * h(t), where sin(2t) x(t) = 2 sin(3t) sin(2t) 3 πt h(t) = πt Find the Fourier transforms of r(t), h(t), and y(t). Note 1: For the problems ii)-iv), you are allowed to use the properties of the Fourier transform provided in the Table 4.1 of the book. state clearly which properties you use. Note 2: For the problems ii)-iv), you are allowed to use the transformation pairs provided in Table 4.2 of the book. You are not allowed to use transformation pairs from the Internet.