Analog encryption algorithms I have a basic understanding of how strong encryption works on digital data. Bits can be changed so that they appear completely random and map one-to-one back to the original set, given the correct decryption key (and possibly other parameters).
But we always talk about digital encryption, never anything that would work on an analog system as far as I know. Good encryption didn't exist until relatively recently (or cryptanalysis would not have been as useful as it was during World War II) while phones and televisions, both using mostly analog signals until the internet came along, have existed for much longer. To my knowledge, nobody seems to have ever come up with secure and practical ways of encrypting them without converting them to a digital signal first.
Upon searching for analog encryption systems I came across DigiCipher (the successor to Videocipher), but it seems to use binary data since Wikipedia mentions that it uses a MPEG-2 compressed stream. Other sites mention that scramblers were used to prevent television channels from being watched by non-paying consumers, but scramblers have little to do with encryption since they (as the name suggests) are not intended to make the message unintelligible. Wikipedia's secure voice article only briefly mentions analog signals and then goes on to describe different digital systems.
The only real analog encryption scheme I found was on that Wikipedia page about secure voice communications. It works by adding noise before transmission and subtracting it on the receiving end. This sounds similar to a one-time pad, but it probably wasn't used only once, which means that all encryption became useless if the phonographic record(s) with the noise were stolen.
Thinking this through, digital encryption algorithms may be used to generate new analog records so that they're no longer a one-time pad. A secret key and variable number (e.g. yymmdd) could be used as input to a digital encryption algorithm, which then produces the noise to be added to the analog signal. Modern (secure) encryption algorithms are not doable by hand at a reasonable speed far as I know though, so I'm not sure how practical this idea is when all you have is mechanical or analog technology. They would have needed a computer.
Have we not (yet) figured out how to securely encrypt signals in a truly analog way (without the use of impractical one time pads), is it impossible (proven, somehow), or are existing algorithms just obscure because there are few applications for them (now that almost everything is digital)?
Some people define "encryption" in such a way as to exclude analog techniques -- there is no such thing as "analog encryption", they would say, because any analog method of obscuring the contents of a transmission is, by their definition, "scrambling", not encryption.

There have been several such scrambling ("analog encryption") techniques, including:

voice scrambling:


some early analog secure voice techniques, as you already mentioned, which added noise (or classic symphony music) from a phonograph at one end, and subtracted the "noise" from an identical, synchronized phonograph at the receiver.
Some analog voice scramblers do frequency inversion
Some analog "rolling code" voice scramblers frequently jump to a new frequency, hopefully faster than any eavesdropper can track, similar to frequency-hopping spread spectrum
Various combinations of the above -- for example, the analog A-3 and the 5B machine built to "decrypt" it which "the speech spectrum was being split into 5 bands, inverted and translated ... the cipher controlling the switching repeated cyclically after 36 sections."
I've heard rumors that some early speech scramblers used an analog vocoder to dissect voice (using a bunch of analog bandpass filters and an analog envelope detector for each one) into a few "control signals", each of which was transmitted on its own (very narrow) analog band (each one independently frequency-hopped, and random gibberish transmitted on unused bands?), and then the received control signals were used to reconstruct an approximation to the original voice.


Some analog "television scrambling" techniques:


Some scrambling systems transmit the visible part of each line exactly the same as normal analog video, but mangle the Horizontal Sync so that standard analog TV receivers can't lock on.
Some scrambling systems invert the black-white luminance of some lines, each line inverted/normal according to a bit from some pseudorandom number generator synchronized with the video signal.
Some scrambling systems invert the red-blue chroma of some lines, each line inverted/normal according to a bit from some pseudorandom number generator synchronized with the video signal.
Several scrambling systems use various combinations of the above.
Videocipher I, Leitch Viewguard, VideoCrypt-S, and Nagravision Syster all scramble video by sending the video scan lines in a scrambled order.
Telefirst ("Tele1st") apparently used some sort of analog scrambling technique (?)
Zenith Z-Tac cable scrambling system apparently used some sort of analog scrambling technique (?)
VideoCrypt I, VideoCrypt II, and Eurocrypt use line cut-and-rotate -- each line of the image is cut into 2 parts and swapped; the exact cutpoint is determined by a pseudo-random sequence generated by a smartcard from a seed value.


All of these systems were developed under severe cost constraints, so they sacrificed some security for lower cost to manufacture legitimate receivers.
So for a long time there was something like an arms race between the "defenders" (pay-per-view broadcasters, military radio manufacturers, etc.) and the "attackers" ( pirate decryption, military codebreakers and cryptanalysts, etc.).