“So far all the discussion of sound has centered on its description as fluctuations in air pressure over time. The representation of sound in the time domain is important to understand, but in some ways it is also awkward. For instance, the frequency of a sound is one of its most important physical properties, but determining frequency from a waveform requires making measurements of time intervals and then doing arithmetic. Indeed, for many complex waveforms, where multiple sinusoids of various frequencies are simultaneously present, it is often unclear where the intervals to be measured begin and end. The frequency domain provides an alternative description of sound in which the time axis is replaced by a frequency axis. In the frequency domain, sounds are represented in a frequency by amplitude and/or phase diagram. “ – ASEL
It’s only complicated if you’re thinking backwards – el Loco Gringo
Do not go wobbly on me here. Do not allow your mind to boggle. Uncle Walter will make it all better. It is the concept which is important not the math. Indeed the math is irrelevant.
Top down thinking assumes that the time domain is reality and the frequency domain is imaginary. As there is much more information to be gained in the frequency domain it is easier to convert the time domain to the frequency domain, get the answer, (in the frequency domain the answer “just is”) and then convert it back. However, this logic tree is fallacious.
Bottom up thinking shows that the frequency domain is reality and the time domain is imaginary. Indeed, a mathematician capable of thinking in the frequency domain (should such a person be possible) might well wonder why in the world would anyone be interested in so limited a concept as an imaginary “time”. (As I wonder why people are so dumb) The reason of course is that in the time domain information can be categorized. Looking at the header time>frequency>time the calculations cancel out and we are left with frequency IE Reality. In fact, the concept of math is, in and of itself, an artifact, a method of categorizing, quantifying, putting things in baskets.
In fact, EVERYTHING we perceive is only an interpretation of what we see. The shadows Plato was talking about.
Sometimes when we can’t make sense out of something we assume that we are dumb. We do not think of the possibility that perhaps there is no sense there. This should set off a flag, but it doesn’t.
NOW is the time to set the algorithm. The “goal” you were looking for in your logic tree. NOW is the time to use top down thinking. NOW you can start with “The frequency domain is reality” and work downwards to see what that implies. (And the implications are staggering) NOW you can put things in baskets. NOW you can quantify, sort, collate, dissect and mangle the data. NOW you can use the scientific method. (not just yet tho)
As profound as this is, the concept of the ANN is profounder.
“A world of beautiful, loving, compassionate people” – Jill Bolte Taylor
That is my gift to humanity – el Loco Gringo
Letters to DrB>Here