Unformatted text preview: itude Fourier Theorem o Proves that every periodic waveform can be expressed in sinusoidal components Can be broken down into a set of harmonics Sum of harmonic components with different amplitudes and phases can construct any kind of signal • Sinusoidal components => fundamental waveforms • In a system, can find out how each different harmonic propagates, and then add them all up to construct how the entire function (signal) propagates o Harmonics are multiples of the fundamental frequency o Signals = Often are periodic waveforms Also think of each periodic signal as a set of amplitudes / frequencies/ phases for all of the harmonic components • There’s no physical difference between sending a complex signal, on the one hand, or sending the full set of harmonic components, on the other, assuming that we are in a linear world (that doesn’t generate additional frequencies beyond those that we are sending in the first place) Fourier analyzer periodic wave form decomposed into amplitudes of the various frequency components Fourier synthesizer put in amplitudes of the various frequency components and generate a complex periodic waveform • Same principle used in keyboards (music synthesizers) o Square wave synthesis Add harmonic oscillations Superposition of the odd sine harmonics with decreasing amplitudes square wave • Overshoots: Gibbs’ phenomenon => there are ways to dampen down these overshoots In order to transmit information, you cannot just send the fundamental frequency (a sine wave) •...
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 Fall '07
 Steier
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