2025-L05su09

2025-L05su09 - 5/27/2009 2003, JH McClel an &...

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Unformatted text preview: 5/27/2009 2003, JH McClel an & RW Schafer 1 ECE2025 Summer 2009 Lectures 5 Fourier Series 27 May 09 5/27/2009 2003, JH McClel an & RW Schafer 3 ANNOUNCEMENTS HW 2 due June 1-2 We do have lecture this Friday (May 29) May 27-28: Turn in Lab 1 Do lab 2 5/27/2009 2003, JH McClel an & RW Schafer 4 FIRST QUIZ Quiz #1, in lecture, Friday, June 5 10% of final grade You can use the full 1:20-2:30 time Review session location/time TBD Coverage: HW #1 and #2 Lectures #1 through #5 (no Fourier series) Might have to read some MATLAB code (wont need to write any) Closed book, closed notes, except: One 8.5X11 sheet allowed, handwritten , OK to write on both sides 5/27/2009 2003, JH McClel an & RW Schafer 5 READING ASSIGNMENTS This Lecture: (we wont finish some slides will be re-presented next lecture). Fourier Series in Ch 3 Fourier Series in Ch 3 Notation: a k for Fourier Series Other Reading: Next Topic: Sampling Recap: Time-Varying Frequency Frequency can change vs. time Continuously, not stepped FREQUENCY MODULATION (FM) FREQUENCY MODULATION (FM) CHIRP SIGNALS Linear Frequency Modulation (LFM) )) ( 2 cos( ) ( t v t f t x c + = VOICE ) 2 cos( ) ( 2 + + = t f t A t x New Signal: Linear FM Called Chirp Signals (LFM) Quadratic phase Freq will change LINEARLY vs. time Example of Frequency Modulation (FM) Define instantaneous frequency QUADRATIC INSTANTANEOUS FREQ Definition For Sinusoid: Derivative of the Angle ) ( ) ( )) ( cos( ) ( t t t A t x dt d i = = Makes sense 2 ) ( ) ( 2 ) ( ) 2 cos( ) ( f t t t f t t f A t x dt d i = = + = + = INSTANTANEOUS FREQ of the Chirp Chirp Signals have Quadratic phase Freq will change LINEARLY vs. time + + = + + = t t t t t A t x 2 2 ) ( ) cos( ) ( + = = t t t dt d i 2 ) ( ) ( CHIRP SPECTROGRAM CHIRP WAVEFORM OTHER CHIRPS (t) can be anything: (t) could be speech or music: FM radio broadcast ) ) cos( cos( ) ( + = t A t x ) sin( ) ( ) ( t t t dt d i = = SINE-WAVE FREQUENCY MODULATION (FM) Look at CD-ROM Demos in Ch 3 5/27/2009 2003, JH McClel an & RW Schafer 14 LECTURE OBJECTIVES Work with the Fourier Series Integral...
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2025-L05su09 - 5/27/2009 2003, JH McClel an &...

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