Re: How does software equlizer works?
OK, let's just ignore all those concerns you raise about fancy state-of-the-art analogue to digital conversion. Let's keep this simple because I'm a simple soul and certainly no mathematician.
We're at the stage now where we have sampled the waveform. All sampling means is that we've decided what number (on the left axis) we are going to attribute to the waveform at any one instant in time, specifically at the sample tick, perhaps every 44,000 times per second. The graph showed a range from 0 to 15, but in fact, that is not anywhere like enough steps on the staircase to say with confidence that the edge of the sine wave is at this step or an adjacent one. It's not a fine enough resolution; in many instances the waveform will indeed have changed between ticks, but due to poor resolution of our simple example, our encoder can't define exactly precisely which step.
So, those clever Philips/Sony engineers conducted tests on better-than-average ears (because the CD was promoted to hi-fi fans initially, so it had be be good technically and sonically) and they decided that what was necessary, assuming that CD was to be a high fidelity carrier, would be not 16 steps but about 64,000 steps*.
As computers work in off-on, yes/no, black/white 1 and 0 logic, the engineers realised by happy coincidence that two eight-bit binary word had enough binary steps in it to code 65,536 steps - a few more than absolutely necessary and by another happy coincidence, the eight bit word was exactly the normal length that computers digested easily - the so-called byte.
A fully saturated (analogue) signal that is as loud as it can be in the computer must sit on the stop step and in binary would have a binary code 1111111111111111 being step 65,536. These two eight-bits bytes combined together all being set to 1 means that the signal is 'fully saturated', and if it was a tiny bit louder or a lot louder, there is no way that the ADC could define that loudness; the signal has used-up all the steps and any loder that the data will be clipped. Conversely, an absolutely silent signal would sit on the very bottom step and would have a binary code 0000000000000000 being step 0.
* Note: history could have played this so very differently. Philips/Sony's marketing departments looked back over the incremental progress of hi-fidelity sound and equipment from the cylinder recorder to FM radio. With each decade and new technology, the frequency response widened, distortion lowered, playing time increased and first stereo then quadrophony (on LP) appeared. To continue the progression - a marketing man's dream situation - all they had to do was to achive a technical standard that was significantly better than the then best analogue system, and they could tap into the accrued goodwill of the high fidelity heritage. But without this heritage they probably would have settled on a much lower technical standard, perhaps only as good as cassettte with only 10,000 steps or so. Lucky for hi-fi that the CD predated the PC by about ten years because otherwise the CD would have primarily been conceived as a bulk data carrier, not a playable audio disk.
I still have my (almost working) Sony CDP-101 player, which I bought the very day CD was launched in the UK - 3 March 1983 (remember it well) and I'd waited years for for the launch of CD. The only other player available that day was the Philips flip-top unit. nce home, I recall comparing my then good turntable with the CD (only three or four disks available that day so not an exact comparison). In fact, on a really fine pressing of music with a moderate loudness and bandwidth that didn't strain my (V15-3) pickup, the sonic differences were relatively small.
Alan A. Shaw
Harbeth Audio UK