3 ms·

S/N for a cassette is variously given as 50dB, 58dB or 67dB [1,2]. Bandwidth is given as 12kHz (standard), 16kH (medium Fi), 19kHz (HiFi) for different quality

by femto 5y ago

S/N for a cassette is variously given as 50dB, 58dB or 67dB [1,2]. Bandwidth is given as 12kHz (standard), 16kH (medium Fi), 19kHz (HiFi) for different quality cassette systems [3]. Let's simplify by assuming the frequency cutoff is a brick wall and the S/N is constant across the band. The maximum channel capacity for a cassette can be calculated using Shannon's Theorem [4]: C = B*log2(S/N+1) Cheap and cheerful (S/N=50dB, B=12kHz): C= 199kbit/s Mid range (S/N=58dB, B=16kHz): C= 297kbit/s Hi Fi (S/N=67dB, B=19kHz): C= 422kbit/s Modern coding (LPDC) can achieve within a fraction of a dB of the Shannon Bound, so those numbers will be close to what a state-of-the-art encoding could do with a cassette. (A new hobby for someone?) [1] http://www.tapeheads.net/showthread.php?t=35390 http://www.tapeheads.net/showthread.php?t=35390 [2] http://www.muzines.co.uk/articles/choosing-a-cassette-tape/1249 http://www.muzines.co.uk/articles/choosing-a-cassette-tape/1... [3] https://arstechnica.com/civis/viewtopic.php?t=848978 https://arstechnica.com/civis/viewtopic.php?t=848978 [3] https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theore... Edit: Here's a dose of reality from another forum: https://dsp.stackexchange.com/questions/70700/why-can-so-little-digital-information-be-stored-on-a-cassette-tape https://dsp.stackexchange.com/questions/70700/why-can-so-lit... My guess is the the Shannon based predictions are realistic, as they are lower than the same rates as achieved by specialised data recording systems. They are also a bit better than what a narrow band radio system can achieve, and a cassette will be a better channel than a typical radio channel.

adrianmonk 5y ago
There's also stereo to consider, right? So you could get up to 2X bandwidth. (Channel separation issues might mean less than 2X in practice, though.) If you want to stretch the definition of "cassette", tapes are two-sided, and there were 4-track recorders that used all 4 tracks in one direction. They weren't anything too exotic. Musicians used them for cheap recordings for demos and such.
- hulitu 5y ago
  You don't want stereo. Only as an error correction maybe.
  - adrianmonk 5y ago
    I'm not a tape expert, but in the spirit of learning more, I did some quick research, and it seems that multi-track tape is very common for data. IBM started doing it in the 1950s and 1960s with 7-track[1] and then 9-track[2] tape. It's still being done today with LTO[3]. --- [1] https://en.wikipedia.org/wiki/IBM_7_track https://en.wikipedia.org/wiki/IBM_7_track [2] https://en.wikipedia.org/wiki/9_track_tape https://en.wikipedia.org/wiki/9_track_tape [3] https://en.wikipedia.org/wiki/Linear_Tape-Open https://en.wikipedia.org/wiki/Linear_Tape-Open
akira2501 5y ago
Another way to look at it, SQNR = 20 * log10(2**Q). When Q=8, equivalent to 8bit PCM encoding, the maximum SNR would be 48db. So the cheap cassettes are like 8bit PCM at 12kHz. Remaining values would be: Q=9, SQNR=54db. Q=10, SQNR=60db. Q=11, SQNR=66db.

by femto 5y ago

adrianmonk 5y ago

There's also stereo to consider, right? So you could get up to 2X bandwidth. (Channel separation issues might mean less than 2X in practice, though.) If you want to stretch the definition of "cassette", tapes are two-sided, and there were 4-track recorders that used all 4 tracks in one direction. They weren't anything too exotic. Musicians used them for cheap recordings for demos and such.

hulitu 5y ago
You don't want stereo. Only as an error correction maybe.
- adrianmonk 5y ago
  I'm not a tape expert, but in the spirit of learning more, I did some quick research, and it seems that multi-track tape is very common for data. IBM started doing it in the 1950s and 1960s with 7-track[1] and then 9-track[2] tape. It's still being done today with LTO[3]. --- [1] https://en.wikipedia.org/wiki/IBM_7_track https://en.wikipedia.org/wiki/IBM_7_track [2] https://en.wikipedia.org/wiki/9_track_tape https://en.wikipedia.org/wiki/9_track_tape [3] https://en.wikipedia.org/wiki/Linear_Tape-Open https://en.wikipedia.org/wiki/Linear_Tape-Open

akira2501 5y ago

Another way to look at it, SQNR = 20 * log10(2**Q). When Q=8, equivalent to 8bit PCM encoding, the maximum SNR would be 48db. So the cheap cassettes are like 8bit PCM at 12kHz. Remaining values would be: Q=9, SQNR=54db. Q=10, SQNR=60db. Q=11, SQNR=66db.