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The waveform produced by sounding a note on most physical instruments will often not exhibit a peak, or will not exhibit the strongest peak, on the note being sounded. Rather, most instruments will instead produce harmonic overtones and our brains fill in the gap of the pitch that’s intended to be sounded.

You can still absolutely deduce the fundamental with great accuracy via an FFT, but the approach is a bit more involved. The relevant research area here is called ‘fundamental frequency estimation’.

For an example of this, you can see this app I built that lets you give keyboard and mouse inputs via playing notes on a bass guitar, which are recognized over the microphone: https://github.com/codyd51/offkeyboard


Hi, author of axle here - thank you for the shout out! It’s been a wonderfully fun and enriching project to work on over the years. I’m now working on XNU at Apple, so won’t be working further on axle for the foreseeable future.


Congrats on the job


One potential hiccup with your one-photino-bird-universe theory (which is quite fun!): I believe I remember a scene in which the ‘birth’ of a photino bird was described. If I remember correctly, it was indeed described as a clone of its parent.


As long as we only see one birth, that's probably fine. It just implies a stable time loop.


What a wonderful thing to say about a stranger's article! Thank you very much for posting this.


Whoa, thank you! I don't know much about RF and learned ad-hoc for this project, and it seems perfectly plausible to me that someone knowledgeable would be able to look at this and identify a root cause - I certainly didn't do anything special for clock recovery, and based on the name I would have blindly assumed that synchronising the carrier wave _would_ be tantamount to recovering the satellite clock. I haven't researched clock recovery yet, and will do so. Once again, thank you!


Thank you for linking this, this course is phenomenal! Several of the videos were immensely helpful in my GPS journey.


Thank you very much for your thoughtful offer! I won't be able to readily work on side projects after starting my new role next week, and am content to consider this project complete for the time being. However, what you've proposed does sound interesting and fun. I'm going to go ahead and shoot an email to the address listed in your profile.


I believe you are correct. My understanding is that the root P key is rotated daily, and needs to be manually uploaded to any military hardware that needs to use it.


Thank you very much! I agree, they are incredible! I really had no idea until making this project, and it makes things like cellular phones so astoundingly impressive.


This project only supports the 'legacy' C/A variant of the NAVSTAR constellation's signals.


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