3 ms·

Thanks again for your detailed comment. I think I understand it now. The only thing slightly puzzling me is why waves are broken up (be it Fourier or in our ear

Thanks again for your detailed comment. I think I understand it now. The only thing slightly puzzling me is why waves are broken up (be it Fourier or in our ears) into sine waves, and not say sawtooth (or some other, like a semicircle as in https://math.stackexchange.com/questions/1019005/what-kind-of-curve-is-made-of-half-circles https://math.stackexchange.com/questions/1019005/what-kind-o...) waveform. I understand how a squarewave needs infinite bandwidth for decomposing into sine waves, but a wave like the semicircle one has a vertical tangent and would not need an infinite bandwidth. Btw you're right, I've never had any signal theory classes (studied mech engg).

vel0city 3y ago
I'm mostly just an amateur myself, so I totally get where you're coming from. FWIW, the graph at the top of that article (as mentioned in the comments) does not have vertical tangents. They're not true semicircles. Most of the answers given to make actual semicircles become non-continuous signals (y >= 0 if ... answer) or infinite sum. The one which doesn't just says they look like semicircles. I don't really have the time (or immediate knowledge, I'm admittedly bad at math) to dig all the math but my gut instinct suggests those aren't true semicircles and don't truly have vertical tangents. And this is kind of how a signal generator can get away making square waves and sawtooths and what not; internally its not always truly "discrete" signals its just quickly flipping a switch from one thing to another. It flips from the high state to the low state fast enough that for your 50MHz oscope it looks pretty continuous, and its probably designed to try and draw a connected line. This all kind of makes some sense when you get into how we actually make electrical signals. We're normally just modulating the electric "vibrations" of some crystal or accelerating some magnet through a loop back and fourth. These things move in continuous waves. As mentioned, things don't have infinite acceleration they take time to shift between states. So you're never going to get something that goes from high to low in zero time. And most home owners will tell you there's no such thing as a right angle. I'd like to mention though, you're imaging the wave as being "broken up" into sine waves, which IMO isn't quite the right way to be looking at it. Its not "breaking up" the signal into sine waves, the signals were always sine waves. Remember my comment, truly square waves don't really exist. We can have things that kinda look square-ish when you squint your eyes, but they're not really square waves. A truly square wave in reality requires infinite acceleration or its not continuous. Fill a bathtub and try to make square waves. Its just not going to happen. I know I'm not fully answering your question, I don't fully know the answer myself. So far in my stumbling around the closest thing I can answer is because that's just how nature and waves are, at least as much as our monkey brains can reason about them. Think about a string in a guitar or a wave in the water or throwing a ball. They all moves in ways which can be described by sine waves. Its just like the nature of how things accelerate and move, changing between states. Why do we see the golden ratio in so many places? Why are circles so special? Good luck on digging for more truth.
- vel0city 3y ago
  sorry, I misused "discrete" in this comment, should say "continuous".

vel0city 3y ago

I'm mostly just an amateur myself, so I totally get where you're coming from. FWIW, the graph at the top of that article (as mentioned in the comments) does not have vertical tangents. They're not true semicircles. Most of the answers given to make actual semicircles become non-continuous signals (y >= 0 if ... answer) or infinite sum. The one which doesn't just says they look like semicircles. I don't really have the time (or immediate knowledge, I'm admittedly bad at math) to dig all the math but my gut instinct suggests those aren't true semicircles and don't truly have vertical tangents. And this is kind of how a signal generator can get away making square waves and sawtooths and what not; internally its not always truly "discrete" signals its just quickly flipping a switch from one thing to another. It flips from the high state to the low state fast enough that for your 50MHz oscope it looks pretty continuous, and its probably designed to try and draw a connected line. This all kind of makes some sense when you get into how we actually make electrical signals. We're normally just modulating the electric "vibrations" of some crystal or accelerating some magnet through a loop back and fourth. These things move in continuous waves. As mentioned, things don't have infinite acceleration they take time to shift between states. So you're never going to get something that goes from high to low in zero time. And most home owners will tell you there's no such thing as a right angle. I'd like to mention though, you're imaging the wave as being "broken up" into sine waves, which IMO isn't quite the right way to be looking at it. Its not "breaking up" the signal into sine waves, the signals were always sine waves. Remember my comment, truly square waves don't really exist. We can have things that kinda look square-ish when you squint your eyes, but they're not really square waves. A truly square wave in reality requires infinite acceleration or its not continuous. Fill a bathtub and try to make square waves. Its just not going to happen. I know I'm not fully answering your question, I don't fully know the answer myself. So far in my stumbling around the closest thing I can answer is because that's just how nature and waves are, at least as much as our monkey brains can reason about them. Think about a string in a guitar or a wave in the water or throwing a ball. They all moves in ways which can be described by sine waves. Its just like the nature of how things accelerate and move, changing between states. Why do we see the golden ratio in so many places? Why are circles so special? Good luck on digging for more truth.

vel0city 3y ago
sorry, I misused "discrete" in this comment, should say "continuous".