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About the wave shaping, if some posters have a hard time visualizing how the mapping looks like: Imagine that you have a (pure) input sine-wave coming up on th

About the wave shaping, if some posters have a hard time visualizing how the mapping looks like: Imagine that you have a (pure) input sine-wave coming up on the y-axis. It then hits some function on the x-y plane, and then gets "reflected" (mapped) onto the x-axis. This imagine explains it quite well, and in this case there's a linear transfer characteristic / operating curve, with no distortion of input signal: https://www.tutorialspoint.com/amplifiers/images/input_cycle.jpg https://www.tutorialspoint.com/amplifiers/images/input_cycle... Now - instead of imaging a perfect linear operating curve, think of how the curve of a diode looks like, and how that would clip the upper curve of input. Now put another diode for the reverse, and you're also clipping the bottom curve of input - this would be a basic diode clipping circuit, which is the fundamental drive-stage for distortion pedals like tube screamers - you'll often see a pair of diodes going opposite directions. (In electronics classes, you tend to learn how to NOT generate distortion - or rather, how to amplify stuff with least amount of distortion possible.)

romwell 6y ago
TL;DR: Wave shaping is just function composition. I don't know why a new term is needed, but if you can visualize function composition for simple functions like floor, min, max, you can visualize wave shaping. If the input signal is f(x), you obtain clipped signal g(x) like this: g(_) = min(1, _) ○ max(-1, _) ○ (a * _) ○ f(_) This can also be written as g(x) = min(1, max(-1, a * f(x))) In the example in the article, T(x) = min(1, max(-1, ax)) is called a transfer function. I find it easier to understand function composition by breaking the functions down into simple parts, though. The sonic effects of this are completely unexplained in the article. Other comments here discuss the effects on harmonics; mathematically, the TL;DR is that the Fourier series of g = t ○ f are more interesting (the intuition why can be obtained by looking at the Fourier series for a square wave). Without getting into math: a clipped signal retains some of the input, and adds more of square wave characteristics. A square wave is the buzz you get by flipping + and - very rapidly, which will force the speaker cone to go all the way in/out very rapidly. The reason why math above doesn't fully represent the effect is that an actual speaker cone won't be able to teleport to min/max positions instantaneously; and the unfaithfulness of the speaker cabinet creates pleasing tonal characteristics.

romwell 6y ago

TL;DR: Wave shaping is just function composition. I don't know why a new term is needed, but if you can visualize function composition for simple functions like floor, min, max, you can visualize wave shaping. If the input signal is f(x), you obtain clipped signal g(x) like this: g(_) = min(1, _) ○ max(-1, _) ○ (a * _) ○ f(_) This can also be written as g(x) = min(1, max(-1, a * f(x))) In the example in the article, T(x) = min(1, max(-1, ax)) is called a transfer function. I find it easier to understand function composition by breaking the functions down into simple parts, though. The sonic effects of this are completely unexplained in the article. Other comments here discuss the effects on harmonics; mathematically, the TL;DR is that the Fourier series of g = t ○ f are more interesting (the intuition why can be obtained by looking at the Fourier series for a square wave). Without getting into math: a clipped signal retains some of the input, and adds more of square wave characteristics. A square wave is the buzz you get by flipping + and - very rapidly, which will force the speaker cone to go all the way in/out very rapidly. The reason why math above doesn't fully represent the effect is that an actual speaker cone won't be able to teleport to min/max positions instantaneously; and the unfaithfulness of the speaker cabinet creates pleasing tonal characteristics.