hw1_complex_num_fourier_transform

# hw1_complex_num_fourier_transform - Massachusetts Institute...

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

hw1_complex_num_fourier_transform - Massachusetts Institute...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online