I have attatched a file called TimeFreq.pdf for your amusement. People think backwards. Lets go back to reality. (we’re diving into bottom up thinking here so hike your panty hose up) What we’re really talking about here is angular momentum. Picture in your mind’s eye a spinning cylinder. Rotate this cylinder in your mind’s eye so you are looking at the end. You have a spinning disk with an axis at the center. The problem is “how can we represent this in a manner such that we can get useful information out of it?”. Lets put a dot on the circumference of this circle. Well that’s better. At least somethings happening. Still can’t get much information out of this, all you can say is that the dot is going round and round and up and down, and you’re starting to get a headache trying to follow it. NOW lets bring out the graph paper. We’ll mark the vertical axis with an arbitrary dimension. In keeping with tradition we’ll call it amplitude. In like manner we’ll mark the other axis with the arbitrary term time. (this is where they get that time as the 4th dimension silliness) Now if we “roll” this circle across the y axis we find that the dot describes a irregular up and down motion. If we factor in the phasing we see a up and down wave is described. We’ll use the arbitrary term sine wave. Now we can measure the amplitudes and time displacement and invent trigonometry. But keep in mind that trig is only a quantification of an interpretation of a perception. In reality all we have is a spinning disk. It is an analogy only. A way of representing a three dimensional process on a piece of paper. Something we can wrap our heads around. This is the time domain.
BUT, hold your water lady, there’s another way to look at this. Let’s draw a variable length arrow from the center of the disk to a point represented by the amplitude. We’ll call this arrow the vector. (direction) Now when we spin the disk we see an arrow going in and out and round and round. Tylenol time again. Now we display this data on an polar coordinate graph (remember the y is vector not time) Now the data is quantifiable without math. Quantification is no longer necessary. So all we have to do is use the Fourier transform to “translate” the time domain data into the frequency domain, get the answer and translate it back without having to worry about that messy old math, or that vacillating arrow that keeps shooting in and out in a vaguely erotic fashion. Don’t even have to worry about the Fourier transform, that’s why god created raster boxes. Just plug the question into the computer and the answer comes out. Something we cannot wrap our heads around. This is the frequency domain.
The math is not the physics.
Letters to DrB>Here