HOMEWORK #1 1. Problem 1.1 2. Problem 1.2 3. Determine if ( ) ( ) ( ) sin 50 sin 200 x t t t = + is periodic and, if so, what is its period? 4. Calculate the Fourier Transform ( ) X ω of x t Ae bt t t at b g b g = ≥ < R S T-cos000 and sketch a graph of the magnitude ( ) X and phase ( ) X ∠ for 1 A a b = = = for 010 ≤ ≤ . 5. Later on in the course we will discuss “window functions” in spectral analysis. When you discretize or sample data from a random process, and you want to compute the Discrete Fourier Transform (DFT), you are actually taking a portion of the data by applying a window to it. The simplest window to use will be a boxcar or rectangular window as defined below for a record of length
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