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ECE2025-L07

# ECE2025-L07 - General Info ECE2025 Spring 2012 Quiz#1 on...

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ECE2025 Spring 2012 Georgia Institute of Technology LECTURE #7 Fourier Series Analysis February 3, 2012 Spring 2012 EE-2025 Spring-2012 jMc-BHJ 2 General Info Quiz #1 on 6-Feb Coverage: up to Lecture #6 Calculators OK, One 8.5” X 11” page of handwritten notes More Problems (w/ solutions) are on the SP-First CDROM web site No make-up test Review session tonight at 6pm Lab #4: also bring headphones Spring 2012 EE-2025 Spring-2012 jMc-BHJ 3 CHIRP SPECTROGRAM Time t t t t t A t x 2 2 ) ( ) cos( ) ( t t t dt d i 2 ) ( ) ( Time Frequency Spring 2012 EE-2025 Spring-2012 jMc-BHJ 4 Spectrogram of Another Chirp ) 1 200 10 ( 2 ) ( 4 t t t Frequency ous Instantane ) 200 40 ( 2 ) ( 3 t t dt d ?

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EE-2025 Spring-2012 jMc-BHJ 5 Sum of Sinusoids ) ( ) ( ) ( 2 1 3 t x t x t x ) ( 2 t x ) ( 1 t x 400 Hz 400 Hz 290 Hz 390 Hz ) ( 3 t x 125ms 125ms Spring 2012 EE-2025 Spring-2012 jMc-BHJ 6 READING ASSIGNMENTS This Lecture: Fourier Series in Ch 3, Sects 3-4, 3-5 Replaces pp. 62-66 in Ch 3 in DSP First Notation: a k for Fourier Series Other Reading: Next Lecture: More Fourier Series Spring 2012 EE-2025 Spring-2012 jMc-BHJ 7 LECTURE OBJECTIVES ANALYSIS via Fourier Series Find elementary components in a signal For PERIODIC signals: x ( t+T 0 ) = x ( t ) Later: spectrum from the Fourier Series Work with the Fourier Series Integral 0 0 0 0 ) / 2 ( 1 ) ( T dt e t x a t T k j T k Spring 2012 EE-2025 Spring-2012 jMc-BHJ 8 HISTORY Jean Baptiste Joseph Fourier 1807 thesis (memoir) On the Propagation of Heat in Solid Bodies
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ECE2025-L07 - General Info ECE2025 Spring 2012 Quiz#1 on...

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