2025-L07 - ECE-2025 Spring-2009 General Info Help Sessions:...

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ECE-2025 Spring-2009 Lecture 7 Fourier Series & Spectrum 30-Jan-2009 eneral Info General Info ± elp Sessions: Mon and Tues 6 at 6pm Help Sessions: Mon and Tues 6 at 6pm ± Office Hours: Visit any Prof or TA ± T-square: square: OFFICIAL ANNOUNCEMENTS & BLOGS ± Quiz #1 on 6 Quiz #1 on 6-Feb Feb ± Coverage: HW #1, #2, #3 and #4 ore Problems (w/ solutions) are on the SP irst CDROM web site ± More Problems (w/ solutions) are on the SP-First CDROM web site ± MATLAB and Lab context will be used for Quiz questions ± Prob Set #4 due NEXTWeek ± Solution to Prob Set #4 will be posted on 5-Feb at 3pm 1/27/2009 EE-2025 Spring-2009 jMc 2 Lecture inusoidal Synthesis Sinusoidal Synthesis ± Use Short-Duration Sinusoids: ± Amp, Phase, Frequency & Duration 1 for ) 2 cos( ) ( + + = k k k k k t t t t f A t x ϕ π ± Freq will change every FRAME ± Then ADD several sinusoids together t k t t k + 1 1/27/2009 EE-2025 Spring-2009 jMc 3 NALYSIS SYNTHESIS ANALYSIS --> SYNTHESIS BREAK INTO FRAMES Amp Phase Freq x(t) FFT: DO FOURIER ANALYSIS Per Frame PUT FRAMES BACK TOGETHER y(t) ADD UP the SINUSOIDS q SMOOTHLY add_cos( ) 1/27/2009 EE-2025 Spring-2009 jMc 4
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ine Synthesis: SPEECH Sine Synthesis: SPEECH ± FRAME Length = 10 millisec ± Examples: p ± Original ± sinusoids per frame 9 sinusoids per frame ± 4 sinusoids ± sinusoids 2 sinusoids ± Need to SMOOTH Boundaries 1/27/2009 EE-2025 Spring-2009 jMc 5 Time-Varying REQUENCIES “Diagram” FREQUENCIES “Diagram” a xi s vertical n cy is th e Freque 1/27/2009 EE-2025 Spring-2009 jMc 6 Time is the horizontal axis INES Spectrogram 4-SINES Spectrogram 1/27/2009 EE-2025 Spring-2009 jMc 7 INES Spectrogram 9-SINES Spectrogram 1/27/2009 EE-2025 Spring-2009 jMc 8
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INES Spectrogram 2-SINES Spectrogram a xi s vertical n cy is th e Freque 1/27/2009 EE-2025 Spring-2009 jMc 9 IME SIGNALS: COMPARE TIME SIGNALS: COMPARE 1/27/2009 EE-2025 Spring-2009 jMc 10 IME SIGNALS: ZOOM TIME SIGNALS: ZOOM 1/27/2009 EE-2025 Spring-2009 jMc 11 Lecture
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2025-L07 - ECE-2025 Spring-2009 General Info Help Sessions:...

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