Exponential Modulation

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Exponential Modulation

• Analog and Digital Communications
• Autumn 2005-2006

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Exponential Modulation

• Modulation in which information signal is encoded
  in carrier frequency or phase
• Amplitude of the transmitted signal is constant
• This modulation is robust to channel gain
  variations
• The modulation is non-linear
• Bandwidth of the transmitted signals depends upon
  the amplitude of the information signal

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Exponential Modulation
Transmitted/Modulated signal
Total instantaneous angle
To obtain angle or exponential modulation
Make instantaneous phase dependent on the
information signal
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Instantaneous Frequency
Instantaneous frequency
For constant phase signals
For signals with time varying phase
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Phase Modulation (PM)
Make phase proportional to the information signal
Instantaneous frequency is dependent on the
derivative of the information signal
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Frequency Modulation (FM)
Make instantaneous frequency dependent on the
information signal
What is the transmitted signal?
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PM to FM and Vice Versa
(For FM)
(For PM)
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Peak and Average Powers

• Peak power is
• Average power is
• Peak to average power ratio is 2
• Compare with DSB and AM
• Low peak to average power ratio is good for
  circuit designers

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AM, FM, and PM Comparison
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Spectral Analysis of FM

• Exponential modulation is non-linear
• Bandwidth of the transmitted signals depends upon
  the amplitude of the information signal
• Hard to analyze with Fourier transforms
• Narrowband approximation makes analysis a little
  easier ? NBFM and NBPM
• For narrowband approximation to hold

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NBFM and NBPM
Consider the bandpass transmitted signal
For narrowband approximation
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NBFM and NBPM
Thus, for NBFM and NBPM
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Tone Modulation
Thus, for NBFM and NBPM
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Tone Modulation with NB
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Tone Modulation with NB
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Tone Modulation with WB