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lec19-handout-6up - 6.003: Signals and Systems Lecture 19...

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6.003: Signals and Systems Lecture 19 November 17, 2009 1 6.003: Signals and Systems DT Frequency Response and Fourier Series November 17, 2009 Mid-term Examination #3 Tomorrow, November 18, 7:30-9:30pm, Walker Memorial (this exam is after drop date). No recitations tomorrow. Coverage: cumulative with more emphasis on recent material lectures 1–18 homeworks 1–10 Homework 10 will not collected or graded. Solutions are posted. Closed book: 3 page of notes ( 8 1 2 × 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Review: Fourier Series and Transforms Harmonic content is natural way to describe some kinds of signals. Ex: musical instruments (http://theremin.music.uiowa.edu/MIS) piano t piano k violin t violin k bassoon t bassoon k Review: Fourier Series and Transforms Representing signals by their frequency components motivates think- ing about systems as “filters.” Example: speech frequency amplitude F1 F2 F3 Electrocardiogram The Fourier transform of the electrocardiogram showed how to de- sign a filter to eliminate unwanted “noise.” 0 : 01 0 : 1 1 10 100 1000 100 10 1 0 : 1 0 : 01 0 : 001 0 : 0001 f = ! 2 [Hz] X ( j ! ) [ V] low-freq. noise cardiac signal high-freq. noise 60 Hz 0 10 20 30 40 50 60   1 0 1 2 t [s] x ( t ) [mV] 0 10 20 30 40 50 60   1 0 1 2 t [s] y ( t ) [mV] DT Fourier series Today: develop similar representations for DT signals and systems. signal processing
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6.003: Signals and Systems Lecture 19 November 17, 2009 2 Signal Processing: Acoustical Prior to the 1970’s, speakers were optimized with mechano- acoustical components, e.g., “bass-reflex” system. driver reflex port Signal Processing: Acoustico-Mechanical Electrovoice Interface A: 8” woofer + 12” “passive radiator” + front and rear tweeters. driver passive radiator Signal Processing: Electronic The development of low-cost electronics enhanced our ability to alter the natural frequency responses of systems. 10 1 10 2 10 3 10 4 10 5 70 80 90 100 110 Frequency (Hz) Magnitude(dB) Eight drivers faced the wall; one pointed faced the listener. “Equalizer” for drivers with limited frequency response (right). Signal Processing: Electronic The development of low-cost electronics enhanced our ability to alter the natural frequency responses of systems. 10 1 10 2 10 3 10 4 10 5 70 80 90 100 110 Frequency (Hz) Eight drivers faced the wall; one pointed faced the listener. “Equalizer” for drivers with limited frequency response (right). Signal Processing Modern audio systems process sounds digitally. A/D DT filter D/A x ( t ) y ( t ) x [ n ] y [ n ] Signal Processing Modern audio systems process sounds digitally. Texas Instruments TAS3004 2 channels 24 bit ADC, 24 bit DAC 48 kHz sampling rate 100 MIPS $7.70 ($4.81 in bulk) Control PWR_DN TEST AINRP AINRM AINLM AINLP 24-Bit Stereo ADC RINA RINB AINRM AINRP AINLM AINLP LINA LINB CS1 SDA SCL Controler GPI0 GPI1 GPI2 GPI3 GPI4 GPI5 24-Bit Stereo DAC CAP_PLL
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lec19-handout-6up - 6.003: Signals and Systems Lecture 19...

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