SPFirst-L02

SPFirst-L02 - 8/22/2003 2003, JH McClellan & RW...

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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 = ) ( 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( + t A f ) 2 ( = 2 1 = = f T A 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 + t ) ( = + t 3 / 20 3 . / 2 / 2 = = = 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 - 8/22/2003 2003, JH McClellan & RW...

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