Clipping creates a waveform that is being
programmed to overshot. What's being chopped off in the clipping, the output digital->analog converter will try to recreate.
(see this Nika Aldrich
paper for explanation of the "hidden over" aspect of digital audio if needed)
The crux is that the output signal is bandwidth limited. Sudden fast changes can't exist anywhere else than inside the computer. A square peak in a row of digital audio sample points does NOT translate to a square topped wave on the output of the DAC. Rather the DAC will reconstruct the waveform peak back to something much like the level it had prior to clipping. In fact, most any processing involving filtering or bandwidth change, mp3'ing and so on, will recreate those 'hidden' peaks.
Try a change of bandwidth, say a sample rate conversion(SRC) from 44.1kHz to 192kHz. Depending on the nature of the clipping, this can easily create peak levels in the waveform that goes several dB's higher than the "brick walled" waveform initially indicates! Attached is an image of a typical loud master, before and after SRC from 44.1 to 192 kHz. Volume was lowered 6dB prior to processing. The sample peak level now indicates 2.5dB higher peak levels.
That's the beauty of clipping(and poor limiting) and probably the reason why many people thinks it sounds better than proper limiting. The clipped waveform doesn't loose all the peak level information. Those peaks are still existing in the digital audio stream, in a modified way, waiting to hit the consumer end where there hopefully is a 1000+ dollars state of the art digital->analog converter. Or not. Research by Nilsen and Lund at TC Electronics, available in the tech library on the TC website, indicates that most consumer CD player DAC's does not handle this abuse. In most cases, what sounds good IS good, but in this case - what sounds good only sounds good on expensive equipment. The master engineer have no possible way to know what's going to happen at the consumer end.
The problem is compounded when there is other processing involved, like a sample rate conversion or a psychoacoustic coding. In the picture example below, the gain was set at -6dB prior to processing to allow headroom for the new and extended peaks that 'suddenly' appeared after the SRC. In most real life conversions, like a consumer coding and decoding an MP3, there will be no headroom since the digital master is already set at maximum digital level. The result is distortion and more clipping.
So what's the solution? You could oversample the wave files to ridiculous degrees to get an idea what the reconstructed wave form looks like. Or.. The neat way: use an oversampled peak meter. If the sample rate is set high enough in the peak meter, it will indicate what's really going on at the output end of the system.
Using a normal PPM along with an oversampled PPM shows this relation between sample values and the real peak values directly. What is gained in the clipping is a direct consequence of pushing the information above the digital ceiling.
Andreas Nordenstam