SPFirst-L03

# SPFirst-L03 - Signal Processing First READING ASSIGNMENTS...

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1/12/2004 © 2003, JH McClellan & RW Schafer 1 Signal Processing First LECTURE #3 Phasor Addition Theorem 1/12/2004 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS ± This Lecture: ± Chapter 2, Section 2-6 ± Other Reading: ± Appendix A: Complex Numbers ± Appendix B: MATLAB ± Next Lecture: start Chapter 3 1/12/2004 © 2003, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES ± Phasors = Complex Amplitude ± Complex Numbers represent Sinusoids ± Develop the ABSTRACTION: ± Adding Sinusoids = Complex Addition ± PHASOR ADDITION THEOREM t j j t j e Ae Xe t z ω ϕ ) ( ) ( = = 1/12/2004 © 2003, JH McClellan & RW Schafer 5 Z DRILL (Complex Arith)

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1/12/2004 © 2003, JH McClellan & RW Schafer 6 AVOID Trigonometry ± Algebra, even complex, is EASIER !!! ± Can you recall cos( θ 1 + θ 2 ) ? ± Use: real part of e j 1 2 ) = cos( θ 1 + θ 2 ) 2 1 2 1 ) ( θ j j j e e e = + ) sin )(cos sin (cos 2 2 1 1 j j + + = (...) ) sin sin cos (cos 2 1 2 1 j + = 1/12/2004 © 2003, JH McClellan & RW Schafer 7 Euler’s FORMULA ± Complex Exponential ± Real part is cosine ± Imaginary part is sine ± Magnitude is one ) sin( )
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## This note was uploaded on 03/03/2010 for the course EE 200 taught by Professor Zadeh during the Spring '08 term at USC.

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SPFirst-L03 - Signal Processing First READING ASSIGNMENTS...

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