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The Ugliness of Privacy Notices
In more than one SF story published decades ago, Robert A. Heinlein had characters transfer audio recordings quickly by "zip-squeal," "60-to-one audio transmission." Of course, Heinlein's original vision of the technology was likely analog (and curiously, if you think about it, assumed his characters could employ a wire or radio channel having a bandwidth of 180 KHz or more, rather than the 3 KHz of a normal telephone line). There were buffers at both ends (such as variable-speed tape).
However(!) Heinlein explicitly added a digital receiving buffer for high-speed audio in The Moon Is A Harsh Mistress (GP Putnam's Sons, 1966). In that book, the narrator, Mannie Davis, asks his self-aware-computer friend, Mike, to allocate a digital memory buffer, "ten-to-the-eighth bits capacity" to receive and store time-compressed audio (along with other data). Mannie then sends Mike compressed audio through a high-bandwidth (and binaural, i.e., stereo) telephone channel, for later playback and analysis at normal speed. There's no question that Heinlein knew about analog-to-digital conversion; in the book he discusses Mike's vocoder and voder (codec) circuits. Indeed, Mannie builds a 20-channel codec for Mike so he can carry on more than one conversation at a time.
Once Ampex invented practical video tape recording, transmitting time-compressed taped video in the same fashion as time-compressed taped audio would have been obvious. (It would also, obviously, have required a heck of a lot of bandwidth, but that's merely a cost-constraint, not a conceptual gap.)
Anyway, Heinlein didn't claim to have invented time-compressed audio transmission. I don't know who did, but it was already in use in the 1950's for radio transmissions by spies, submarines, and so-forth, to frustrate attempts to locate the transmitter by radio direction-finding (by minimizing the time DF'ers would get to take bearings on the transmitted signal).
Information Source: American Heritage of Invention & Technology, Spring 1997, Volume 12/Number 4
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"They began talking about radio control for torpedoes. The idea itself was not new, but her concept of "frequency hopping" was. Lamarr brought up the idea of radio control. Antheil's contribution was to suggest the device by which synchronization could be achieved. He proposed that rapid changes in radio frequencies could be coordinated the way he had coordinated the sixteen synchronized player pianos in his Ballet M�éanique. The analogy was complete in his mind: By the time the two applied for a patent on a "Secret Communication System," on June 10, 1941, the invention used slotted paper rolls similar to player-piano rolls to synchronize the frequency changes in transmitter and receiver, and it even called for exactly eighty-eight frequencies, the number of keys on a piano.