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21
Support - (fb2k) / Re: DLNA
Last post by abax2000 -
Currently, only foo_out_upnp is installed (with which I had the short lucky spell).
Still no honey.

Probably success or failure depends on the devices involved (and how every brand implements DLNA).
Any Samsung experience around?
24
Scientific Discussion / Re: Help me understand why sound is one dimensional
Last post by Rotareneg -
Or put very simply:

A linear array of data has one dimension as it requires only a single number to specify which piece of data is being considered. The data contained within the array is irrelevant to the dimensionality of the array itself: It could be a sequence of air pressure measurements (aka sound,) 3D models for a game, video files, forum posts, or a mix of any and all of that. All that matters is that each piece of data is referenced by a single number.
26
Scientific Discussion / Re: Help me understand why sound is one dimensional
Last post by polemon -
If that is your idea of an image, then I would say that a point sound source - or a "point" as a model for an eardrum - would be 0D rather tham 1D ...
But rather than claiming "0D", I would say that your model of an "image" might be wrong or at least not in line with your model of soumd.
Each point in the image carries a compound of (time-) frequencies. So: if you insist on "time" in a sound waveform, why don't you insist on time in the light waveform?

There are at least two answers to that latter question. 1: In how the human eye projects colour down to a triplet. But that is how humans work, not what is emitted. 2: In that you think that sound changes over time; "music", not just "chord". But then the analogy should be motion picture rather than image.
I'm not sure this is helping, but that aside, the "0D" is a bit conflated in mathematics, rather if you think of something having no dimension, they're simply non-dimensional, or: scalar. A point has no dimensional attributes. A point might be addressed by coordinates and return a scalar, or higher-dimension value.

For instance you can map one 2D space into another, a common example is the conversion of polar coordinates into Cartesian coordinates, and back. Cartesian coordinates are points defined by x and y, while polar coordinates are defined by r and θ (where θ is an angle).

To convert from polar to Cartesian, you'd do: f(r, θ) = {r * cos(θ), y * sin(θ)} → {x, y}
To convert from Cartesian to polar, you'd do: g(x, y) = {sqrt(x² + y²), atan(y/x)} → {r, θ}
I.e. both functions take two values, and return two values, one 2D point, returns a 2D number.

In terms of an RGB color bitmap image, you could say that each x and y coordinate for each pixel, returns three values: r, g, b. Of course we can map this number onto a linear scale (since most are limited for all color spaces), but theoretically the color plane is infinite, and cannot be linearized like we do in a fixed color gamut, like 24-bit color, etc. So in these terms, the pixel coordinates in a color picture, return a three-dimensional number value. In case we have a grayscale image, where each pixel is just one number, each pixel coordinates return a scalar value.

Each higher-order value, can be composed of an arbitrary number of dimensions, including scalar. In cases of an RGB color image, each two dimensional pixel coordinate, of which each component is scalar, maps to a three-dimensional value, where each component of that value is a scalar as well.

A point has no length or area or volume. A single point only defines itself. A line is defined by at least two points in n-dimensional space, it may have a length, but no area or volume. A plane is defined by at least three points, which are not on the same gradient as the other two. Planes may have areas, but no volume. And finally a space needs at least four points, etc.
Higher order objects also exist, things like hypercubes, in 4D space, etc. Anything of a higher order than a point, is a set of points.

I believe this is kinda where the confusion of Op comes from. Plotting a waveform is essentially a function that maps all values of a 1-dimensional discrete function into a 2-dimensional discrete plane, where each valid point in the mapped function is assigned one color, and each invalid point no color (background).

Having said that, the statement "Sound is one-dimensional" is incredibly ambiguous. In terms of signal definitions it is, but in terms of propagation in space it isn't. So, yeah...
27
General Audio / Beats Per Minute
Last post by triumphtrident -
   How can I add a heading for BPM? The data is readily available from Mixmeister or other sites. I just don't see a method for doing it.
28
FLAC / Re: EAC Task Completed ALWAYS finishes on 99.9%
Last post by chamill -
^ Thanks for replying to me. I will have to double-check that when I get home later tonight and I'll post on here.

The CD drive finishes completely and my Hard Disk Lights stop blinking. So it's as though it's 100% complete but I don't get the 100% complete indicator.

I'll see if that changes with the over read setting.
30
Scientific Discussion / Re: Help me understand why sound is one dimensional
Last post by polemon -
Yes, in terms of waveforms signals in the time domain are one dimensional.

If you think of a discrete-time signal - which I assume you're more familiar with - for each sample in a stream of samples, each one has a value. So, your projection function is s(x) -> y, where s(x) is your sample list, x the sample, and y the sample value at point x.

A two-dimensional plot of a function like this. i.e. mapping y for every x, is a mapping. Mappings may or may not produce additional "dimensions" for perception's sake.

If you think of an image, you're thinking of a matrix of values, each corresponding to a pixel (discussing this in terms of bitmaps is a bit easier, here). So, each column (we'll call that x) and each row (we'll call that y), maps to a color (let's call that z).

Assuming we have a grayscale picture, you can map each (x,y) point in that matrix to its pixel value as brightness, giving you that image. However you might think of it as a contour plot, mapping each value of each (x,y) point on axis z, that would result in a 3-dimensional plot. Both are valid, however depending on how we understand the mapping, he might get an image in one instance, or a 3-dimensional plot in another.

Now, let's take a step back from discrete-time signals. I'm assuming you're familiar with the sinusoidal function sin(x).
now, let's define a function, which is quite simply: f(x) = sin(x). Now, as we can see from the function definition and the function signature, that it takes only one variable, in this case x. The return value of f(x), we might call y, giving us: y = sin(x). We can now plot this function on a 2D plane, but notice what we're doing here: we're plotting the input and output values of a one-dimensional function onto a 2d plane!

A two-dimensional function might look like this: f(x,y) = sin(x) * y. If we want we can assign the return value of f(x,y) to z, we can think of x, y, and z as coordinates in a 3D plot, however, that depends on how we want to map that function. It is important to note, that both our first and this second example, the function map to a scalar value, however this is not always necessarily a requirement.

Things like FFT, returns a two-dimensional number for each set of input numbers.

Harking back to the one-dimensional-ness of a discrete-time signal, like PCM, we can think of the entire audio file or whatever, as a string of values, like a list. Each item in that list can be addressed by only one coordinate: it's time index. Say our audio chunk is one hundred samples long, and lets call that list 's'. Now, let's use some list/array notation here, so with something like s{x} I can get the value of s at position x. To plot each value, we might say: y = s{x}, so each point x in s is returned and plotted on the y axis. Note, that we're not addressing that point with x and y, y is merely the result or value at position x! Instead we address the value of y ONLY with x! Furthermore (the f(x) = sin(x) being a good example here), note that for each input of x, we get a defined and single result. However, the result would return an array of values if we'd try to map in reverse!

If you have further questions, feel free to ask further questions.

Any representation of data which consists of 2 coordinates for each data point is 2-dimensional. In order to uniquely specify a point, you must give 2 coordinates or there would be confusion.
Incorrect.
Case in point: f(x) = sin(x)
You're confusing coordinate and return value. The return value is defined by its coordinate, which in case of a simple sinusoid, is only one-dimensional. You can map input coordinates and its return values onto a 2D plane, sure, but this doesn't make the function two-dimensional.

A signal waveform must have 2 coordinates, or else the numerous times a signal has the same amplitude would be indistinguishable from one another.
Incorrect.
Case in point: f(x) = sin(x)
Periodic functions like sinusoids, are perfectly fine having the same return value every 2π. While the function has periodically the same return value, doesn't mean the signal or whatever other function is invalid. In case of continuous-time domain signals, this is pretty much the only way this actually works. However even lower order functions express this behaviour: f(x) = x², returns 2 for both x = 2 and x = -2. Yet, we can trivially plot these functions on a 2D plane.

A 1-dimensional data representation would have only the single number to unambiguously specify each point. One example of this would be the x- or y-coordinate axis by itself.  A 1-dimensional representation of data is almost useless by itself; it only becomes useful when used as a reference for another data set (value on a number line).  Once it is referenced to 2 other data sets (such as the x and y coordinates of a signal existing in time) it is then a 2-dimensional data set.
Incorrect.
Another simple way of thinking of 1-dimensional structures is strings:
Let's define the string S = "Hello, World". Let's further assume, that the first value starts with 0.
In that case I can access each letter by only one dimension: S{0} = 'H', S{1} = 'e', S{2} = 'l', S{3} = 'l', and so forth.
Note that even though S{2} and S{3} have the same return value (both times 'l') this doesn't invalidate the data structure being one-dimensional.

Your math professor friend is either confused, or is confusing you with his explanation.
No, it makes perfect sense, and is pretty much defined in every single school-type math book, like that. I believe the confusion is down to understand mappings and representations, and actual dimensions of a function.

You can also plot a 3D image on a 2D plane (such as your monitor rendering a 3D object in a game), it does work, because we can either use projection (in that case a rendering pipeline), or some other means (like mapping f(x) = x² onto a piece of paper). Drawing a 3D cube on a piece of paper, doesn't make the cube 2D, neither does drawing the function f(x) = x² as y = x² onto a piece of paper two-dimensional.
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