I've mentioned Codec 2 a few times in the past, but for those who don't rememember, David Rowe has been working on a very low bitrate codec optimized for speech applications. This is of interest in amateur radio because we don't have a suitable speech codec which isn't patent encumbered (if for instance, DSTAR's AMBE codec was not encumbered by patents, we could create open source versions which would be compatible with the DSTAR network).
David just announced that's he's got the codec down to 1400 bits per second. Check it out: it sounds pretty good.
Even if you are't interested in amateur radio, there are reasons to think this might be useful. David says that:
- At 1400 bit/s you can send 45 phone calls in the same bandwidth required for a standard 64 kbit/s phone channel.
- 1400 bit/s is 175 bytes/second
- A 30 second voice mail can be stored in 5250 bytes
- A 30 minute pod cast can be stored in 308 kbytes.
Courtesy of Phil Harvey’s Puzzle « Programming Praxis, I discovered that the numbers from 1..16 can be partitioned into two 8 element sets, with these nifty identities!
2+3+5+8+9+12+14+15 == 1+4+6+7+10+11+13+16
22+32+52+82+92+122+142+152 == 12+42+62+72+102+112+132+162
23+33+53+83+93+123+143+153 == 13+43+63+73+103+113+133+163
There has to be a good way to use this to make a cool geometric puzzle as well.\
Bonus: Are there any other values of N such that the numbers from 1..N can be split into two sets, each of which have the same sum, sum of squares, and sum of cubes?
Spoiler: Yes, there are.