MIT6_003S10_lec14_handout

MIT6_003S10_lec14_handout - 6.003: Signals and Systems...

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bassoon t 6.003: Signals and Systems 6.003: Signals and Systems Fourier Representations March 30, 2010 Fourier Representations Fourier series represent signals in terms of sinusoids . leads to a new representation for systems as filters . Lecture 14 March 30, 2010 Mid-term Examination #2 Wednesday, April 7, 7:30-9:30pm. No recitations on the day of the exam. Coverage: Lectures 1–15 Recitations 1–15 Homeworks 1–8 Homework 8 will not collected or graded. Solutions will be posted. Closed book: 2 pages of notes ( 8 1 2 × 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Review sessions during open office hours. Fourier Series Representing signals by their harmonic components. ω ω 0 2 ω 0 3 ω 0 4 ω 0 5 ω 0 6 ω 0 0 1 2 3 4 5 6 harmonic # DC fundamental second harmonic third fourth fifth sixth Musical Instruments Harmonic content is natural way to describe some kinds of signals. Ex: musical instruments (http://theremin.music.uiowa.edu/MIS) piano cello bassoon t t t oboe horn altosax t t t violin t 1 252 seconds 1 Musical Instruments Harmonic content is natural way to describe some kinds of signals. Ex: musical instruments (http://theremin.music.uiowa.edu/MIS) piano k cello k bassoon k oboe k horn k altosax k violin k
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± ² ² ² ² 6.003: Signals and Systems Lecture 14 March 30, 2010 Musical Instruments Harmonic content is natural way to describe some kinds of signals. Ex: musical instruments (http://theremin.music.uiowa.edu/MIS) piano piano t k violin violin t k bassoon bassoon t k Harmonics Harmonic structure determines consonance and dissonance. octave (D+D’) fifth (D+A) D+E ± time(periods of "D") harmonics 0123456789101112 0123456789101112 –1 0 1 D D' D A D E 0123456789 01234567 Harmonic Representations Harmonic Representations What signals can be represented by sums of harmonic components? Is it possible to represent ALL periodic signals with harmonics? What about discontinuous signals?
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This note was uploaded on 11/07/2011 for the course ELECTRICA 6.003 taught by Professor Staff during the Summer '10 term at MIT.

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MIT6_003S10_lec14_handout - 6.003: Signals and Systems...

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