2025-L02su09 - ECE2025 Summer 2009 LECTURE#2 Sinusoids Time and Phase Shift Adding Sinusoids 15 May 09 2003 rws/jMc 2 License Info for SPFirst

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Unformatted text preview: ECE2025 Summer 2009 LECTURE #2 Sinusoids Time and Phase Shift Adding Sinusoids 15 May 09 5/19/2009 2003 rws/jMc 2 License Info for SPFirst Slides ¡ This work released under a Creative Commons License with the following terms: ¡ Attribution ¡ The licensor permits others to copy, distribute, display, and perform the work. In return, licensees must give the original authors credit. ¡ Non-Commercial ¡ The licensor permits others to copy, distribute, display, and perform the work. In return, licensees may not use the work for commercial purposes—unless they get the licensor's permission. ¡ Share Alike ¡ The licensor permits others to distribute derivative works only under a license identical to the one that governs the licensor's work. ¡ Full Text of the License ¡ This (hidden) page should be kept with the presentation 5/19/2009 2003 rws/jMc 3 ANNOUNCEMENTS ¡ If you’re just tuning in, be sure to read the assorted administrative notes from the previous lecture - see T- square. ¡ First recitations are either (special case for this week only!) ¡ Today (Wed) for L01 and L02 ¡ Tomorrow (Thursday) for L03, L04, L05, and L06 ¡ Rest of recitations will be either Monday (for L01 and L02 ) or Tuesday (for L03, L04, L05, and L06) 5/19/2009 2003 rws/jMc 4 READING ASSIGNMENTS ¡ This Lecture: ¡ Chapter 2 ¡ Other Reading: ¡ Appendix A: Complex Numbers ¡ Appendix B: MATLAB ¡ Next Lecture: start Chapter 3 5/19/2009 2003 rws/jMc 5 LECTURE OBJECTIVES ¡ Sinusoids! ¡ Write general formula for a “sinusoidal” waveform, or signal. ¡ From the formula, plot the sinusoid versus time ¡ Define Sinusoid Formula from a plot. ¡ Relate TIME-SHIFT to PHASE. ¡ Brief review of complex numbers. ¡ Adding sinusoids. 5/19/2009 2003 rws/jMc 6 ¡ Always use the COSINE FORM ¡ Sine is a special case: ) ) 440 ( 2 cos( ϕ π + t A SINES and COSINES ) cos( ) sin( 2 π ω ω − = t t 5/19/2009 2003 rws/jMc 7 SINUSOIDAL SIGNAL ¡ FREQUENCY ¡ Radians/sec ¡ Hertz (cycles/sec) ¡ PERIOD (in sec) ¡ AMPLITUDE ¡ Magnitude ¡ PHASE A t cos( ) ω ϕ + ω A ϕ ω π = ( ) 2 f T f = = 1 2 π ω 5/19/2009 2003 rws/jMc 8 EXAMPLE of SINUSOID ¡ Given the Formula ¡ Make a plot ) 2 . 1 3 . cos( 5 π π + t 5/19/2009...
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This note was uploaded on 01/24/2010 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Institute of Technology.

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2025-L02su09 - ECE2025 Summer 2009 LECTURE#2 Sinusoids Time and Phase Shift Adding Sinusoids 15 May 09 2003 rws/jMc 2 License Info for SPFirst

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