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Signals, Fourier Series

Signals, Fourier Series. Analog and Digital Communications Autumn 2005-2006. Review of Signals and Spectra. A generic sinusoidal signal Phasor representation Frequency domain representation Rotating phasors Frequency plots Amplitude Phase. Amplitude. Phase. Amplitude. Phase.

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Signals, Fourier Series

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  1. Signals, Fourier Series Analog and Digital Communications Autumn 2005-2006 CS477: Analog and Digital Communications

  2. Review of Signals and Spectra • A generic sinusoidal signal • Phasor representation • Frequency domain representation • Rotating phasors • Frequency plots • Amplitude • Phase Amplitude Phase CS477: Analog and Digital Communications

  3. Amplitude Phase Review of Signals and Spectra • Two sided spectra can be seen from • This represents two rotating phasors • Amplitude and phase spectrum (two sided) CS477: Analog and Digital Communications

  4. Periodic Signals • A signal is periodic if there exists such that • Smallest such is called fundamental period • Any integer multiple of is also a period CS477: Analog and Digital Communications

  5. Average signal and Power • Average signal • Average power • For periodic signals, limit goes away CS477: Analog and Digital Communications

  6. Fourier Series Representation • Projection of periodic signals onto basis functions • Periodic signal is a weighted sum of these basis functions • Exponentials are used as basis functions for writing Fourier series • Any periodic signal can be expressed as a sum of infinite number of exponentials (or sinusoids for real signals) CS477: Analog and Digital Communications

  7. Fourier Series (Each term represents one frequency) (fundamental frequency) Line spectra at frequencies that are integer multiple of fundamental frequency CS477: Analog and Digital Communications

  8. Sinc Function Note the points where this function becomes zero Where does this appear? CS477: Analog and Digital Communications

  9. Fourier Series: Example Amplitude normalized by A/4 CS477: Analog and Digital Communications

  10. Sinusoidal Fourier Series • For real signals • and can be expressed in terms of CS477: Analog and Digital Communications

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