THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM

Frequency Modulation: Introduction and Concepts

Tom Rondeau

([email protected])

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 Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Amplitude Modulation

Tom Rondeau ([email protected]) GR FM 3 / 38 AM Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Double Sideband, Suppressed Carrier

Tom Rondeau ([email protected]) GR FM 4 / 38 AM Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Double Sideband, Suppressed Carrier

Tom Rondeau ([email protected]) GR FM 5 / 38 AM Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Double Sideband (With Carrier)

Tom Rondeau ([email protected]) GR FM 6 / 38 AM Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Double Sideband (With Carrier)

Tom Rondeau ([email protected]) GR FM 7 / 38 AM Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Single Sideband (Upper)

Tom Rondeau ([email protected]) GR FM 8 / 38 AM Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Single Sideband (Vestigial)

Tom Rondeau ([email protected]) GR FM 9 / 38 AM Signaling THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Problem with noise: Information in amplitude

Tom Rondeau ([email protected]) GR FM 10 / 38 AM Signaling THE 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 Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM FMing a Sine Wave

Tom Rondeau ([email protected]) GR FM 13 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Frequency Modulation:

Continuous Time  Z t  y(t) = cos 2πf∆ x(τ)dτ 0

Discrete Time   f∆ X y[n] = cos 2π x[n] fs

 X  f∆ y[n] = cos η x[n] , η = 2π fs We call η the sensativity.

Tom Rondeau ([email protected]) GR FM 14 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM FMing a Sine Wave: fs = 800 ksps, f∆ = 5 kHz, fm = 1 kHz

Tom Rondeau ([email protected]) GR FM 15 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM FMing a Sine Wave fs = 800 ksps, f∆ = 75 kHz, fm = 1 kHz

Tom Rondeau ([email protected]) GR FM 16 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM FMing a Sine Wave fs = 800 ksps, f∆ = 75 kHz, fm = 15 kHz

Tom Rondeau ([email protected]) GR FM 17 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Bessel Functions!

WAT!

Tom Rondeau ([email protected]) GR FM 18 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM No, let's skip that.

Ok, good.

Tom Rondeau ([email protected]) GR FM 19 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM More practically speaking, what's the signal bandwidth?

Denitions  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 Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM What's the practical dierence?

Filter to the bandwidth of the dierent rules

Tom Rondeau ([email protected]) GR FM 21 / 38 Frequency Modulation THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM What's the practical dierence?

Not much.

Actually running into numerical issues with oat32's it's so close.

Tom Rondeau ([email protected]) GR FM 22 / 38 Frequency Modulation THE 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 FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Spectrum Allocation

Tom Rondeau ([email protected]) GR FM 25 / 38 Broadcast FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM AM and FM Bands

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Tom Rondeau ([email protected]) GR FM 26 / 38 Broadcast FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM FM Spectrum and Information Composition

Tom Rondeau ([email protected]) GR FM 27 / 38 Broadcast FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Modulating Stereo FM

Tom Rondeau ([email protected]) GR FM 28 / 38 Broadcast FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Demodulating Stereo FM

Tom Rondeau ([email protected]) GR FM 29 / 38 Broadcast FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Channelizing FM

Tom Rondeau ([email protected]) GR FM 30 / 38 Broadcast FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Single-Channel Spacing (bad)

Tom Rondeau ([email protected]) GR FM 31 / 38 Broadcast FM THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Empty Channel Between Stations

Tom Rondeau ([email protected]) GR FM 32 / 38 Welcome to radio free America. - Happy Harry Hardon (Christian Slater), Pump Up the Volume Pirate Radio THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Pirates on the airwaves

Tom Rondeau ([email protected]) GR FM 34 / 38 Pirate Radio THE 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 Radio THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM What's the issue?

High demand for spectrum. Interference and the FM Capture Eect.

Tom Rondeau ([email protected]) GR FM 36 / 38 Pirate Radio THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Exploring the FM Capture Eect

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 of transmitter. Pirate station: E310 running FM broadcast. Android App remotely controls system. Changes any E310 radio parameter.

Tom Rondeau ([email protected]) GR FM 37 / 38 Conclusion THE FREE & OPEN SOFTWARE RADIO ECOSYSTEM Questions?

So be it.

Tom Rondeau ([email protected]) GR FM 38 / 38