Imaginary numbers samples

[steve]

What if audio samples were allowed to be imaginary/complex numbers?

The problem with this statement is that “audio sample” has a precise definition. It is a time + value pair, where both time and value are real numbers, so by definition an “audio sample” cannot be imaginary / complex numbers. You may choose to define a “thing” as a time / value pair where one or both may be imaginary, but that “thing” is not an “audio sample” in the accepted sense of the concept.

That’s like saying “addition” has a precise definition as an operation on real numbers.

No, it’s like saying that “letters of the alphabet” has a precise definition, and that “numbers” are not "letters of the alphabet. To say “what if letters of the alphabet could be numbers?” requires that you redefine what “alphabet” means.

[steve]

What if audio samples were allowed to be imaginary/complex numbers?

The problem with this statement is that “audio sample” has a precise definition. It is a time + value pair, where both time and value are real numbers, so by definition an “audio sample” cannot be imaginary / complex numbers. You may choose to define a “thing” as a time / value pair where one or both may be imaginary, but that “thing” is not an “audio sample” in the accepted sense of the concept.

That’s like saying “addition” has a precise definition as an operation on real numbers.

You missed the most important part of Trebor’s message:

Sound waveform only runs in one direction: forwards in time.

Both Trebor and myself are saying that your proposition of “Imaginary numbers samples” is nonsense.

Consider how audio playback works. In short:

• Sample values are converted to a voltage that is applied to the speaker coil, cause a mechanical displacement of the speaker cone, which causes air to move.

So what do you expect an imaginary number to do? Create an imaginary voltage, causing an imaginary displacement of the the speaker cone, thus creating imaginary sound waves? Think about it - it’s nonsense.

[Piotr_Grochowski]

Consider how audio playback works. In short:

• Sample values are converted to a voltage that is applied to the speaker coil, cause a mechanical displacement of the speaker cone, which causes air to move.

So what do you expect an imaginary number to do? Create an imaginary voltage, causing an imaginary displacement of the the speaker cone, thus creating imaginary sound waves? Think about it - it’s nonsense.

It’s physical:

Move 1 right = move right
Move -1 right = move left
Move i right = move up
Move -i right = move down

Which perfectly makes sense. And it can as well be applied to physical speakers. What’s the problem?

[steve]

What’s the problem?

What’s the make and model number of the loudspeakers that handle imaginary voltages?

[DVDdoug]

We are still talking about sound & soundwaves. If you come-up with a way of generating sound with imaginary numbers, and maybe you can, it’s still a sound that can be recorded and played back without imaginary numbers (or without any “numbers” at all if you have an analog tape recorder).

If you want to learn more about “math & audio” there is a FREE online book called [u]The Scientist and Engineer’s Guide to Digital Signal Processing, by By Steven W. Smith[/u].

[Piotr_Grochowski]

What’s the problem?

What’s the make and model number of the loudspeakers that handle imaginary voltages?

The physical example of complex numbers movement should also extend to voltages.

[Piotr_Grochowski]

We are still talking about sound & soundwaves. If you come-up with a way of generating sound with imaginary numbers, and maybe you can, it’s still a sound that can be recorded and played back without imaginary numbers (or without any “numbers” at all if you have an analog tape recorder).

If you want to learn more about “math & audio” there is a FREE online book called [u]The Scientist and Engineer’s Guide to Digital Signal Processing, by By Steven W. Smith[/u].

As I said, generation of a real numbers sound with imaginary numbers is irrelevant to this topic because this topic is about complex numbers sound. Those spectrograms are merely transforming the imaginary part into the frequency domain, not into the amplitude.

[DVDdoug]

As I said, generation of a real numbers sound with imaginary numbers is irrelevant to this topic because this topic is about complex numbers sound.

OK I DON’T know that this topic is about, but have fun with your imaginary/complex sounds!

I’m guessing you don’t know how to program but if you understand the math you can use MATLAB (or one of the free MATLAB clones) to make any equation, expression or function that you can “imagine”, and play it as sound or make a WAV file etc.

…I think you’re on your own. This discussion is going nowhere and there’s not much point it talking about or thinking about what some imaginable/unimaginable sound might sound like. You’ll need to generate some sounds mathematically and listen to the results, and you’ve been given several suggestions about how to do that.