THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Frequency Modulation:
Introduction and Concepts
Tom Rondeau
2016-02-01
�It is proved that the frequency
modulation system using a spacing or
compensating wave is inferior to the
amplitude variation system both as to
the width of the frequency band
occupied and as to distortion of signal
wave form.�
- John R. Carson, "Notes on the Theory
of Modulation"
AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Amplitude Modulation
Tom Rondeau ([email protected]) GR FM 3/ 38
AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Double Sideband, Suppressed Carrier
Tom Rondeau ([email protected]) GR FM 4/ 38
AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Double Sideband, Suppressed Carrier
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AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Double Sideband (With Carrier)
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AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Double Sideband (With Carrier)
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AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Single Sideband (Upper)
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AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Single Sideband (Vestigial)
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AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Problem with noise: Information in amplitude
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AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Problem with noise: Noise changes amplitude
Tom Rondeau ([email protected]) GR FM 11 / 38
�This superiority will increase as
methods of dealing with ignition noise,
either at its source or at the receiver,
are improved�
- Edwin H. Armstrong, "A Method of
Reducing Disturbances in Radio
Signaling by a System of Frequency
Modulation"
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
FMing a Sine Wave
Tom Rondeau ([email protected]) GR FM 13 / 38
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Frequency Modulation:
Continuous Time
y(t) = cos
(2πf∆
∫t
0x(τ)dτ
)
Discrete Time
y [n] = cos
(2π
f∆
fs
∑x [n]
)
y [n] = cos(η∑
x [n]), η = 2π
f∆
fs
We call η the sensativity.
Tom Rondeau ([email protected]) GR FM 14 / 38
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
FMing a Sine Wave:fs = 800 ksps, f∆ = 5 kHz, fm = 1 kHz
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Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
FMing a Sine Wavefs = 800 ksps, f∆ = 75 kHz, fm = 1 kHz
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Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
FMing a Sine Wavefs = 800 ksps, f∆ = 75 kHz, fm = 15 kHz
Tom Rondeau ([email protected]) GR FM 17 / 38
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Bessel Functions!
WAT!
Tom Rondeau ([email protected]) GR FM 18 / 38
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
No, let's skip that.
Ok, good.
Tom Rondeau ([email protected]) GR FM 19 / 38
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
More practically speaking, what's the signalbandwidth?
De�nitions � Assumes sinusoid input
f∆: maximum frequency deviation from the carrier
fm: the highest frequency component in the original signal
Carson's Rule
BT = 2(f∆ + fm)
Generally assumed to under-represent the signal bandwidth
Carlson's Rule
BT = 2(f∆ + 2fm)
More realistic calculation of the bandwidth
Tom Rondeau ([email protected]) GR FM 20 / 38
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
What's the practical di�erence?
Filter to the bandwidth of the di�erent rules
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Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
What's the practical di�erence?
Not much.
Actually running into numerical issues with �oat32's it's so close.
Tom Rondeau ([email protected]) GR FM 22 / 38
Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
What about with a real song?
Tom Rondeau ([email protected]) GR FM 23 / 38
�The thrill, believe me, is as much in the
battle as in the victory.�
- David Sarno�
Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Spectrum Allocation
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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
AM and FM Bands
`
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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
FM Spectrum and Information Composition
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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Modulating Stereo FM
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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Demodulating Stereo FM
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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Channelizing FM
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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Single-Channel Spacing (bad)
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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Empty Channel Between Stations
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�Welcome to radio free America.�
- Happy Harry Hardon (Christian
Slater), Pump Up the Volume
Pirate RadioTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Pirates on the airwaves
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Pirate RadioTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Pirates!
Cultural
Play music you and your community want.
Political
Talk religion and politics.
Ecomonic
Sell local ads.
Localization
The Internet is too large, too global.
Restricted to a geographic niche.
Ownership of medium and equipment.
Tom Rondeau ([email protected]) GR FM 35 / 38
Pirate RadioTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
What's the issue?
High demand for spectrum.
Interference and the FM Capture E�ect.
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Pirate RadioTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Exploring the FM Capture E�ect
Receiver Station:
Standard GNU Radio FM receiver with B210.
FM �Broadcaster�:
Android device connected to B200.GNU Radio app on Android.Controls frequency and gain of B200; FM sensitivity oftransmitter.
Pirate station:
E310 running FM broadcast.Android App remotely controls system.Changes any E310 radio parameter.
Tom Rondeau ([email protected]) GR FM 37 / 38
ConclusionTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM
Questions?
So be it.
Tom Rondeau ([email protected]) GR FM 38 / 38