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How do signals at double the frequency indicate a video signal?

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    This seems to be asking for a scientific explanation, which is off-topic here but may be on-topic elsewhere. – Edlothiad Jan 5 '18 at 15:47
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    @NKCampbell scientifically, they don’t (either that or I should’ve failed my degree) this may be IU but it definitely sounds OOU – Edlothiad Jan 5 '18 at 16:19
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    Actually it is explained in the novel: the message consists of two kinds of signals (say long and short burst), and the total number of bursts is the product of two prime numbers, say p and q: so the scientists draw a pxq grid, and paint black the long bursts, so an image appears, and so on... – Luca Jan 5 '18 at 16:21
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    In the movie, you're actually mingling two events in quick succession. Kent hears a minor disturbance in the rather full blast primes transmission that identifies the second signal (harmonics?) Ellie then gets the feed from that second signal on the spectrum analyzer, and looking at the shape of the second signal, identifies it as a video feed and calls for the tv. I don't know enough about radio signals to know why, but having to be familiar with every earth-source radio wave to filter out false positives probably helped (it WAS earth video, after all) – Radhil Jan 5 '18 at 16:37
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    Both the script (scifiscripts.com/scripts/contact.txt) and the book have lots of info about how they knew. Honestly I think someone with a better grasp of the technology than me should answer this one, though – Valorum Jan 5 '18 at 22:18
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I don't claim to be an expert, but I can try to explain this in my limited fashion.

Some old radio receivers used to have two modes of operation: AM and FM. AM stands for "amplitude modulation" and FM stands for "frequency modulation". We can emit radio waves of different amplitudes and wavelengths, and by changing them frequently we can encode signals. E.g. a region of higher amplitude or greater frequency would indicate 1, and the reverse would indicate 0. Using this we can encode anything, provided enough bandwidth.

There's also another type of modulation - polarisation modulation. The novel explains it well, in my opinion:

"When a wave of light comes at you--visible light, radio light, any kind of light--it's vibrating at right angles to your line of sight. If that vibration rotates, the wave is said to be elliptically polarized. If it rotates clockwise, the polarization is called right-handed; counterclockwise, it's left-handed. I know it's a dumb designation. Anyway, by varying between the two kinds of polarization, you could transmit information. A little right polarization and that's a zero; a little left and it's a one. Follow? It's perfectly possible. We have amplitude modulation and frequency modulation, but our civilization, by convention, ordinarily just doesn't do polarization modulation."
Contact by Carl Sagan

As you see, with three different types of polarisation one can have three signals in one. As far as I understand, the signal received from Vega was an AM signal containing the prime numbers. It's commonly believed that a natural phenomenon could not generate the prime sequence just like that, so it must be a sign of intelligent life (from the script, with a hat tip to Valorum for finding it):

                    FISHER
        Linearly polarized; a set of moving
        pulses restricted to two different
        amplitudes --

So the two amplitudes corresponded to binary numbers, and when converted to the decimal system they yielded the prime numbers. Later, David Drumlin suggests they also check the polarisation modulation:

                    ELLIE
        ... could it be a nested code of
        some sort?

                    DRUMLIN
        You must have checked the signal for
        polarization modulation already...

Ellie hesitates.  Drumlin looks at her.  Whoops.

                    ELLIE
        Dr. Lunacharsky...?

                    LUNACHARSKY
               (takes a drag)
        Analyzing signal polarization
        shifts.

He type in a series of commands.  Something begins to
happen on the main display --

                    LUNACHARSKY
        Bingo.

POV - THROUGH WINDOW

Kitz, on the phone, sees the activity around the console.

BACK TO SCENE

Lunacharsky types in commands as he talks.

                    LUNACHARSKY
        A second layer, nested within the
        main signal; possibly... a picture?
        Product of three primes...

                    KITZ
               (joining them)
        What.

                    LUNACHARSKY
        ... definitely three dimensions,
        either a hologram or a two-
        dimensional picture that moves in
        time; a movie.

                    DRUMLIN
               (dryly)
        Hope there's a cartoon.

                    KITZ
        How is that possible?  How could all
        that information be encoded in --

                    KENT
        Well, sir, some bits of the signal
        are bits that tell us how to
        interpret the other bits.
        Technically speaking.

JURYRIGGED 35-INCH MONITOR

Strings of zeros and ones fill the screen as the group
assembles around it.

                    ELLIE
        Enlarge.

Willie types.  Ellie moves closer, studying it.
Intuitively:

                    ELLIE
        Try plotting values in a three
        dimensional coordinate system.

A pattern begins to emerge.

                    DRUMLIN
        Throw a gray scale on it; standard
        interpolation.

                    ELLIE
        Rotate 90 degrees counterclock wise.

Willie enters commands.  All are mesmerized by the shadows
taking form on the screen.

                    ELLIE
        It has to be an image.  Stack it up,
        string-breaks every 60th character.

On the screen a distinct black and white moving image
forms; grays define it even further.  The group is
transfixed.  Kitz whispers to an aide who makes a call in
a hand radio.

                    KENT
        Um... I've got an auxiliary sideband
        channel here.  I think it's audio.

The "auxiliary sideband" Kent refers to is also a nifty trick. The modulation process isn't 100% efficient, so the power that was supposed to go to one specific frequency or amplitude may "leak" to a slightly higher or lower frequency or amplitude. By changing the amount of leakage, one could encode another message using the sideband.

Later Arroway says there's another, weaker signal "underneath" the previous two, though she doesn't disclose the method:

"Ms. President, sorry to be late, but I think we've just hit the cosmic jackpot. We've.. It's... Let me try and explain it this way: In classical times, thousands of years ago, when parchment was in short supply, people would write over an old parchment, making what's called a palimpsest. There was writing under writing under writing. This signal from Vega is, of course, very strong. As you know, there's the prime numbers, and `underneath' them, in what's called polarization modulation, this eerie Hitler business. But underneath the sequence of prime numbers and underneath the retransmitted Olympic broadcast, we've just uncovered an incredibly rich message--at least we're pretty sure it's a message. As far as we can tell, it's been there all along. We've just detected it. It's weaker than the announcement signal, but I'm embarrassed we didn't find it sooner."
From the novel

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