ECE2025-L05 - General Info about Quiz ECE2025 Lecture #5...

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ECE2025 Spring 2012 School of Electrical & Computer Engineering Georgia Institute of Technology Lecture #5 Spectral Representation January 27, 2012 General Info about Quiz Quiz #1 on Feb-06-2012 at lecture time in the same lecture hall Closed-book test; 4 problems Bring your calculator; no online connections; no MATLAB; no cellphones; no iPad; no PDA… One 8.5x11 sheet of hand-writing notes allowed Coverage: up to periodic signals; mainly HW1 thru 3 and slightly beyond; no Fourier series 2 Spring 2012 ECE-2025 Spring-2012 BHJ READING ASSIGNMENTS This Lecture: Chapter 3, Section 3-1 Other Reading: Appendix A: Complex Numbers Next Lecture: Ch 3, Sects 3-2, 3-3, 3-7 & 3-8 3 Spring 2012 ECE-2025 Spring-2012 BHJ LECTURE OBJECTIVES Sinusoids with DIFFERENT Frequencies SYNTHESIZE by Adding Sinusoids SPECTRUM Representation Graphical Form shows DIFFERENT freqs N k k k k t f A t x 1 ) 2 cos( ) ( 4 Spring 2012 ECE-2025 Spring-2012 BHJ
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FREQUENCY DIAGRAM Plot Complex Amplitude vs. Freq 0 100 250 –100 –250 freq (in Hz) 3 / 7 j e 3 / 7 j e 2 / 4 j e 2 / 4 j e 10 Complex amplitude Spectral line How many sinusoids are there? What are their mathematical expressions? 5 Spring 2012 ECE-2025 Spring-2012 BHJ Another FREQ. Diagram Frequency is the vertical axis Time is the horizontal axis A-440 A musical scale consists of a discrete set of frequencies. 6 Spring 2012 ECE-2025 Spring-2012 BHJ Euler’s Formula Reversed Solve for cosine (or sine) ) sin( ) cos( t j t e t j ) sin( ) cos( t j t e t j ) sin( ) cos( t j t e t j ) cos( 2 t e e t j t j ) ( ) cos( 2 1 t j t j e e t 7 Spring 2012 ECE-2025 Spring-2012 BHJ “INVERSE” Euler’s Formula Solve for cosine (or sine) Interpret as sum of two rotating phasors going in opposite directions cos( t ) 1 2 ( e j t e j t ) sin( t )
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ECE2025-L05 - General Info about Quiz ECE2025 Lecture #5...

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