hw1_complex_num_fourier_transform - Massachusetts Institute...

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.02 Intro to EECS II Spring 2008 Homework #1: Complex numbers, Fourier Series, Fourier Transform Issued: February 8, 2008 Due: February 15, 2008 Copyright © 2007 by M.H. Perrott and C.G. Sodini 1. For the following exercises on complex numbers, assume j =− 1 . a. Write simplified expressions for jj , jjj ,and jjjj . b. Draw a labeled plot of vector z where 12 zj = + and the x-axis and y-axis correspond to the real and imaginary components, respectively. Be sure to include labels for the magnitude and phase (in degrees as opposed to radians ) of z . c. Calculate the magnitude, K , and phase (in radians ), Φ , of z ,where j zK e j Φ = =+ d. Calculate the real component, a , and imaginary component, b , for 4/ 6 6 j aj b e π += 2. For the following exercises on Fourier Series, use only the complex exponential form of the Fourier Series: x ( t ) = ˆ X n e jn ω o t n =−∞ ˆ X n = 1 T x ( t ) e jn o t dt t o t o + T a. Calculate the Fourier Series ˆ X n for ( ) ( ) () s
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This note was uploaded on 08/23/2009 for the course EECS 6.02 taught by Professor Terman during the Spring '08 term at MIT.

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hw1_complex_num_fourier_transform - Massachusetts Institute...

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