Things like waveforms and time domain signals are one dimensional. Signal transformation through things like FFT is also one dimensional but returns a two-dimensional value.

I'm surprised how many people don't realize this, but the FFT returns the same number of dimensions as you put in, so a 1D function has a 1D FFT. It's a linear transform, so you get the same number of points and dimensions between domains. I suspect that the misconception you have hear (that frequency is somehow of higher dimensionality than time in spite of them having inverse units) is related to the general confusion most people have on this topic.

Well, a Fourier Transform (discrete or continuous) returns a complex-valued function, which real and imaginary components can be mapped onto a 2D plane. Complex numbers by definition extend the one-dimensional number line in \mathbb{R}, to the two-dimensional comlpex-plane \mathbb{C}. That's what I was referring to. Then again, judging by how things were discussed here, I doubt most participants have grasped the concept of complex numbers...

People have such a limited ability to grasp what a 3D sound field is that most do not realize they even exist. The perception of sound is basically 1D with a bit of stereo, and this is the thing people are talking about. And they do mean to say 1D, they're just not sure what the words mean and are expressing themselves incorrectly.

Well, I'm not sure we're talking about perception of sound here. When Op started the thread, I thought we talk about sound as in the way signals are expressed. Hence I tried to clarify in that direction. Perhaps I should've given this a pass.

Last post by j7n -
The visualization boxes indeed do not have borders since the interface was "flattened" for Windows 10 in the current version. The boxes had a "sunken" style like an embedded LCD display. When the toolbars are locked, the visualization touches the left side of its parent toolbar. They were never correctly centered, but now it is more obvious. Some UI panels and splitters have a new option Border > Standard, which makes them look closer to the 1.3 version, but nothing like that for the toolbar boxes. I guess you have to roll with the times and accept the metro style.

Last post by jsdyson -
I uploaded some wonderful demos -- fairly hard for a real DolbyA to decode nearly as clearly. I grabbed material which has lots of opportunity for intermodulation, possible stereo image smearing/shift, mirrored (quick echo) voices, and just vocal reproduction in general. A lot of this older material seems to have significant vocal emphasis -- but I think that you might agree that the sound is pretty good. In recent days the decoder has gotten more correct LF behavior (so true LF like Scarborough Fair is much better), and also the distortion sidebands as created by a changing gain slew are mostly cancelled now.

I cannot claim that the results are impressive -- but they are darned good. The decoder really does well considering that some people say that it is impossible.

The only frustrating thing is that the site that I use limits the mp3 to 200kbits/sec and any mp3 causes a significant loss of the subtle detail.

The full feature and quality decoder will be available sometime in the future. Right now, the currently available 'free' version still does okay for casual use, but the very enhanced and completed version is very significantly better. Hopefully, there will be something released as a plugin.

I still think the confusion is down to the rather inappropriate usage of the term "sound". It doesn't determine what realm we're discussing in here right now.

From the replies to this thread, I think the real problem is people not understanding what dimensions are.

Things like waveforms and time domain signals are one dimensional. Signal transformation through things like FFT is also one dimensional but returns a two-dimensional value.

I'm surprised how many people don't realize this, but the FFT returns the same number of dimensions as you put in, so a 1D function has a 1D FFT. It's a linear transform, so you get the same number of points and dimensions between domains. I suspect that the misconception you have hear (that frequency is somehow of higher dimensionality than time in spite of them having inverse units) is related to the general confusion most people have on this topic.

Sound propagation through air is a multivariate problem, where sound is propagated in three dimensions, changes through time, and returns a sound pressure for each point at any given point, that's a four-dimensional function.

People have such a limited ability to grasp what a 3D sound field is that most do not realize they even exist. The perception of sound is basically 1D with a bit of stereo, and this is the thing people are talking about. And they do mean to say 1D, they're just not sure what the words mean and are expressing themselves incorrectly.

Last post by VEG -
I tested foobar2000 v1.4b19, and I have noticed that visualizations on toolbar don't have native borders anymore, and now they use just white background. It doesn't fit standard Windows theme. Is there a way to return back these borders and backgrounds?

Last post by polemon -
I still think the confusion is down to the rather inappropriate usage of the term "sound". It doesn't determine what realm we're discussing in here right now. Things like waveforms and time domain signals are one dimensional. Signal transformation through things like FFT is also one dimensional but returns a two-dimensional value.

Sound propagation through air is a multivariate problem, where sound is propagated in three dimensions, changes through time, and returns a sound pressure for each point at any given point, that's a four-dimensional function.

Similar things happen when looking at RF signal propagation through space.

So, perhaps it's a good idea to first define the kinda frame we're discussing here?

The output of a line out jack is literally a 1D linear array of speaker displacements. If you could not represent sound as a linear sequence of driver positions, speakers would not work.

Conversely, what is the motion of a diaphragm in a microphone that generates a waveform?