SPFirst-L02

SPFirst-L02 - © 2003 JH McClellan& RW Schafer 1 Signal...

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Unformatted text preview: 8/22/2003 © 2003, JH McClellan & RW Schafer 1 Signal Processing First LECTURE #2 Phase & Time-Shift Complex Exponentials 8/22/2003 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS ¡ This Lecture: ¡ Chapter 2, Sects. 2-3 to 2-5 ¡ Appendix A: Complex Numbers ¡ Appendix B: MATLAB ¡ Next Lecture: finish Chap. 2, ¡ Section 2-6 to end 8/22/2003 © 2003, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES ¡ Define Sinusoid Formula from a plot ¡ Relate TIME-SHIFT to PHASE t j Xe t z ω = ) ( Introduce an ABSTRACTION : Complex Numbers represent Sinusoids Complex Exponential Signal 8/22/2003 © 2003, JH McClellan & RW Schafer 5 SINUSOIDAL SIGNAL ¡ FREQUENCY ¡ Radians/sec ¡ or, Hertz (cycles/sec) ¡ PERIOD (in sec) ¡ AMPLITUDE ¡ Magnitude ¡ PHASE ) cos( ϕ ω + t A f ) 2 ( π ω = ω π 2 1 = = f T A ϕ ω 8/22/2003 © 2003, JH McClellan & RW Schafer 6 PLOTTING COSINE SIGNAL from the FORMULA ¡ Determine period : ¡ Determine a peak location by solving ¡ Peak at t=-4 ) 2 . 1 3 . cos( 5 π π + t ) ( = +ϕ ω t 3 / 20 3 . / 2 / 2 = = = π π ω π T 8/22/2003 © 2003, JH McClellan & RW Schafer 7 ANSWER for the PLOT ¡ Use T=20/3 and the peak location at t=-4...
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SPFirst-L02 - © 2003 JH McClellan& RW Schafer 1 Signal...

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