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THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Frequency Modulation:

Introduction and Concepts

Tom Rondeau

(tom@trondeau.com)

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 (tom@trondeau.com) GR FM 3/ 38

AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Double Sideband, Suppressed Carrier

Tom Rondeau (tom@trondeau.com) 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)

Tom Rondeau (tom@trondeau.com) GR FM 6/ 38

AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Double Sideband (With Carrier)

Tom Rondeau (tom@trondeau.com) GR FM 7/ 38

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

Tom Rondeau (tom@trondeau.com) GR FM 10 / 38

AM SignalingTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Problem with noise: Noise changes amplitude

Tom Rondeau (tom@trondeau.com) 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 (tom@trondeau.com) 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 (tom@trondeau.com) GR FM 14 / 38

Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

FMing a Sine Wave:fs = 800 ksps, f∆ = 5 kHz, fm = 1 kHz

Tom Rondeau (tom@trondeau.com) GR FM 15 / 38

Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

FMing a Sine Wavefs = 800 ksps, f∆ = 75 kHz, fm = 1 kHz

Tom Rondeau (tom@trondeau.com) GR FM 16 / 38

Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

FMing a Sine Wavefs = 800 ksps, f∆ = 75 kHz, fm = 15 kHz

Tom Rondeau (tom@trondeau.com) GR FM 17 / 38

Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Bessel Functions!

WAT!

Tom Rondeau (tom@trondeau.com) GR FM 18 / 38

Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

No, let's skip that.

Ok, good.

Tom Rondeau (tom@trondeau.com) 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 (tom@trondeau.com) 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

Tom Rondeau (tom@trondeau.com) GR FM 21 / 38

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 (tom@trondeau.com) GR FM 22 / 38

Frequency ModulationTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

What about with a real song?

Tom Rondeau (tom@trondeau.com) 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

Tom Rondeau (tom@trondeau.com) GR FM 28 / 38

Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Demodulating Stereo FM

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Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Channelizing FM

Tom Rondeau (tom@trondeau.com) GR FM 30 / 38

Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Single-Channel Spacing (bad)

Tom Rondeau (tom@trondeau.com) GR FM 31 / 38

Broadcast FMTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Empty Channel Between Stations

Tom Rondeau (tom@trondeau.com) GR FM 32 / 38

�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

Tom Rondeau (tom@trondeau.com) GR FM 34 / 38

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 (tom@trondeau.com) 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.

Tom Rondeau (tom@trondeau.com) GR FM 36 / 38

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 (tom@trondeau.com) GR FM 37 / 38

ConclusionTHE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Questions?

So be it.

Tom Rondeau (tom@trondeau.com) GR FM 38 / 38