HW2 - BIM 281 Homework 02 Due date: Friday, 05/09/08 1....

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1 1. Calculate the (continuous) Fourier transform of ( ) sin5 cos3 gx x x = . Sketch this transform in a “3D”-plot whose “ y ”- and “ z ”-axis represent the transform’s imaginary and real part, respec- tively, whereas the “ x ”-axis represents frequency. Prepare a separate sketch for the magnitude spectrum of this transform. (Hint: No integration is required; instead, results from the lectures and previous homework can be applied. (In particular problem 2 of HW 1 should get you started.) Make sure your sketches use the actual frequency f and not the angular frequency. Label all parts of your sketches ade- quately, including the positive directions of the axes. Note: Pay special attention to the small details in this relatively easy problem!) 2. Consider the function () 1i f 1 0i f1 x x = < . a. Sketch a graph of . b. Use the definition of the continuous Fourier transform to calculate ( ) Gf . (Include all steps of your derivation.
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HW2 - BIM 281 Homework 02 Due date: Friday, 05/09/08 1....

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