Analog Sinusoidal Modulation

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Analog Sinusoidal Modulation
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Single-Carrier Modulation Methods

• Analog communication
• Transmit/receive analog waveforms
• Amplitude Modulation (AM)
• Freq. Modulation (FM)
• Phase Modulation (PM)
• Quadrature Amplitude Mod.
• Pulse Amplitude Modulation

• Digital communication
• Same but treat transmission and reception as
  digitized
• Amplitude Shift Keying (ASK)
• Freq. Shift Keying (FSK)
• Phase Shift Keying (PSK)
• QAM
• PAM

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Radio Frequency (RF) Modem

• Message signal stream of bits
• Digital sinusoidal modulation in digital
  signaling
• Analog sinusoidal modulation in carrier circuits
  for upconversion to RF

Error Correction
Digital Signaling
D/A Converter
SignalProcessing
CarrierCircuits
Transmission Medium
Carrier Circuits
SignalProcessing
s(t)
r(t)
TRANSMITTER
RECEIVER
CHANNEL
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Modulation

• Modulation some characteristic of a carrier
  signal is varied in accordance with a modulating
  signal
• For amplitude, frequency, and phase modulation,
  modulated signals can be expressed as
• A(t) is real-valued amplitude function
• fc is carrier frequency
• ?(t) is real-valued phase function

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Amplitude Modulation by Cosine
Review

• Multiplication in time convolution in Fourier
  domain (let w0 2 p f0)
• Sifting property of Dirac delta functional
• Fourier transform property for modulation by a
  cosine

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Amplitude Modulation by Cosine
Review

• Example y(t) f(t) cos(w0 t)
• Assume f(t) is an ideal lowpass signal with
  bandwidth w1
• Assume w1 ltlt w0
• Y(w) is real-valued if F(w) is real-valued
• Demodulation modulation then lowpass filtering
• Similar derivation for modulation with sin(w0 t)

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Amplitude Modulation by Sine
Review

• Multiplication in time is convolution in Fourier
  domain
• Sifting property of the Dirac delta functional
• Fourier transform property for modulation by a
  sine

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Amplitude Modulation by Sine
Review

• Example y(t) f(t) sin(w0 t)
• Assume f(t) is an ideal lowpass signal with
  bandwidth w1
• Assume w1 ltlt w0
• Y(w) is imaginary-valued if F(w) is real-valued
• Demodulation modulation then lowpass filtering

lower sidebands
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Amplitude Modulated (AM) Radio

• Double sideband large carrier (DSC-LC)
• Carrier wave varied about mean value linearly
  with baseband message signal m(t)
• ka is the amplitude sensitivity, ka gt 0
• Modulation factor is ? ka Am where Am is
  maximum amplitude of m(t)
• Envelope of s(t) has about same shape as m(t) if
• ka m(t) lt 1 for all t
• fc gtgt W where W is bandwidth of m(t)

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Amplitude Modulation

• Disadvantages
• Redundant bandwidth is used
• Carrier consumes most of the transmitted power
• Advantage
• Simple detectors (e.g. AM radio receivers for
  cars)
• Receiver uses a simpleenvelope detector
• Diode (with forwardresistance Rf ) in series
• Parallel connection ofcapacitor C and
  loadresistor Rl

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Amplitude Modulation (cont)

• Let Rs be source resistance
• Charging time constant (Rf Rs) C must be short
  when compared to 1/ fc, so (Rf Rs) C ltlt 1/ fc
• Discharging time constant Rl C
• Long enough so that capacitor discharges slowly
  through load resistor Rl between positive peaks
  of carrier wave
• Not so long that capacitor voltage will not
  discharge at max rate of change of modulating
  wave 1/fc ltlt Rl C ltlt 1/W

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Other Amplitude Modulation Types

• Double sideband suppressed carrier (DSB-SC)
• Double sideband variable carrier (DSB-VC)
• Single sideband (SSB) Remove either lower
  sideband or upper sideband by
• Extremely sharp bandpass or highpass filter, or
• Phase shifters using a Hilbert transformer

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Quadrature Amplitude Modulation

• Allows DSB-SC signals to occupy same channel
  bandwidth provided that the two message signals
  are from independent sources
• Two message signals m1(t) and m2(t) are sent
• Ac m1(t) is in-phase component of s(t)
• Ac m2(t) is quadrature component of s(t)

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Frequency Modulated (FM) Radio

• Message signal analog audio signal
• Transmitter
• Signal processing lowpass filter to reject above
  15 kHz
• Carrier circuits sinusoidal modulatation from
  baseband to FM station frequency (often in two
  modulation steps)
• Receiver
• Carrier circuits sinusoidal demodulation from FM
  station frequency to baseband (often in two
  demodulation steps)
• Signal processing lowpass filter to reject above
  15 kHz

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Frequency Modulation

• Non-linear, time-varying, has memory, non-causal
• For single tone message m(t) Am cos(2 p fm t)
• Modulation index is ? ?f / fm
• ? ltlt 1 gt Narrowband FM (looks like
  double-sideband AM)
• ? gtgt 1 gt Broadband FM

Instantaneous frequency
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Carson's Rule

• Bandwidth of FM for single-tone message at fm
• Narrowband
• Wideband
• Carsons rule for single-tone FM
• For a general message signal, fm W

FM Radio TV Audio
?f fm ? Peak freq. deviation (?F) Peak message freq. (W) Deviation ratio (D) Bandwidth BT 2 fm (1? ) Station Spacing 75 kHz 15 kHz 5 180 kHz 200 kHz 25 kHz 15 kHz 1.66 80 kHz 6 MHz
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Summary

• General form of modulation

Modulation A(t) ?(t) Carrier Type Use
DSB-LC DSB-SC DSB-VC SSB ?0 ?0 ?0 Yes No Yes No Amp. Amp. Amp. Amp. AM Radio Marine Radios
QAM No Hybrid Satellite comm.
Phase Frequency AcAc No No Angle Angle FM Radio
h(t) is the impulse response of a bandpass filter
or phase shifter toeffect a cancellation of one
pair of redundant sidebands.
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Angle Modulation
Optional

• Angle modulation general form
• Ac is constant carrier amplitude
• ?i(t) is instantaneous angle of modulation in
  radians
• Average frequency inrad/s over interval Dt
• Instantaneousfrequency in rad/s
• Instantaneous angle
• Phase modulation
• Frequency modulation