Do we grasp 'frequency domain' as opposed to 'time domain'?

[weaver]

Do many people here have a good grasp of 'frequency domain' as opposed to 'time domain' in the context of the representation and manipulation of sound?

This issue has come up in a number of threads here where we are looking at visual representations of sound; what does each axis of a graphical representation tell us and how should we interpret what we see. I am comfortable with the representation of a sine wave on a graph which has amplitude as its vertical axis and time as its horizontal and the fact that from that representation, assuming that the relevant scales are included, we can derive information about the frequency of that wave.

The basic principles of digital audio: that we can divide the time axis into regular intervals (such as 44100 times a second for CD) and similarly with the amplitude axis where the interval between samples results in the 'bit depth', are things that (I think) are fairly straightforward to visualise - see for example the wiki page on pulse code modulation.

But, once we get to 'spectrum analysis' and further when I finally realised that MP3 coding was done in the frequency domain the visualisation gets a bit more difficult.

As I understand it, this means looking at amplitude with respect to frequency rather than to time and that's something I haven't quite got hold of. Clearly 'time' still has to come into it somewhere.

The purpose of the thread is to identify the most basic principles that are not widely understood; if everyone else on HUG is completely happy with swapping between time and frequency domains then all well and good.

[honmanm]

I'm OK with the concept but it would be great to have an explanation in layman's terms as Fourier analysis is an incredibly useful tool for understanding what has happened to a signal (wish I could remember more from Uni days).

[T.W.]

I'm also not an expert but I'll give it a try. This is what's inside my head and what I remember - not sure if this is correct.

In the time domain you look at a system to see how it changes over the time. If you play a recording then you are probably in the time domain and the music changes over the time. If you want to encode this recording digitally and if you want to do this in the time domain, then you can only build a (digital) value for the amplitude of the signal every time
the clock ticks (sampling rate) But this is already what the digital encoding of analog signals does (PCM). So this doesn't help us that much for a compressed version like MP3 ...

Fortunately there are some mathematics that may help us here like FFT. You look at the signal for a very short time and then you assume that the signal has the same pattern forever. Then you transform the signal into the frequency domain.

This means that you don't care about time any more since you assumed that the signal lasts forever. Doing this is similar to what a prism does with sunlight. The result is the frequency spectrum of our signal in a short amount of time.

Since you already have digital information from PCM it doesn't seem to matter how long it take to run the algorithm. But it matters how long each segment of the signal is that you analyse with each iteration of your algorithm.

Then MP3 seems to analyse the result of our transformation and tries to find a "compressed" version of the data. In our prism an sunlight example we could use less colors and less shades to let the result look the same to our eyes. I have no idea how this works in MP3 and what it's actually doing.

The final step is then to transform it back to the time domain (mathematically) and to create a new representation for our signal that has almost the same "sound" as the original one, but needs less space for storage.

Again - this is just what's inside my head ....

[weaver]

Since you already have digital information from PCM it doesn't seem to matter how long it take to run the algorithm. But it matters how long each segment of the signal is that you analyse with each iteration of your algorithm.

Does this mean that, by definition, frequency domain information has a 'built in' sample rate or is there such a thing as 'analogue' frequency domain?

[T.W.]

Does this mean that, by definition, frequency domain information has a 'built in' sample rate or is there such a thing as 'analogue' frequency domain?

It may be better to stop guessing here ... Please read about MP3 in wikipedia. Look for "MP3". There is an English version here: http://en.wikipedia.org/wiki/Mp3_encoder and a german version here http://de.wikipedia.org/wiki/MP3
The German version is easier to understand (if you speak German :-) but you can try to translate it online. Internet explorer -> right mouse click -> translate with live search. The result is pretty good.
The chapter "Datenkomprimierung" - translated "Data compression" may help you to understand what's going on.

Good luck
T.W.