You need these for the measurement: 1. a simulated load (or even real load if you do not mind your headphones playing extremely loud sine waves) 2. a signal generator 3. an analyzer with an input that is suitable for testing the output of the amplifier at its maximum level 4. a digital...

  Another (in my opinion not unlikely) possibility is that the "clear" differences you heard are mainly the result of expectation bias and simple factors by level differences.     That is why the test should ideally be performed by people who do expect to hear differences. You could try...

  Another solution is to delay the input by half sample with sinc interpolation. This is basically the same as upsampling to 88.2 kHz, except the output does not include samples that would be the same (with linear phase filtering) as the input signal. Inter-sample peaks are not necessarily...

  With synthetic test signals, the inter-sample peaks can be made very high, but such peaks are unlikely to occur in real music that is not already heavily compressed and clipped (and in that case, it is not even obvious whether having the inter-sample peaks above 0 dBFS is correct or not, as...

  The upsampling is only used to find out what the inter-sample peaks would be (approximately) at the original sample rate. The exact level of the peaks depends on the reconstruction filter used, so it is actually not the same for all DACs.

  It is likely to be clipping if runs of multiple samples are at 0 dBFS, and I think Audacity has an option for detecting this. Also, if a histogram of the sample values peaks at 0 dBFS, then it suggests clipping as well (as it can be seen on the 2008 version of this track). Without any dynamic...

I was originally referring to the clipping that possibly occurs when decoding lossy compressed audio.   Nevertheless, clipping is not uncommon in commercial music either, because of the loudness war.

  In other words, they can. Of course, converting the output to an integer format limits it to 0 dBFS, but that is already clipping of the actual sample values.

With the lossy codecs, it is not just inter-sample clipping, but clipping can occur already on the PCM stream as some samples could exceed 0 dBFS.

  Sample and hold is not the same as linear interpolation. If we consider all samples being represented as "infinitely" short impulses (so that in the frequency domain the passband is mirrored between the Nyquist frequency and the sample rate, and then this repeats infinitely at Fs intervals...

Power levels are in watts, but the actual output power in W (which depends on a number of other factors) does not matter here, as we ultimately only need the ratio of the peak and the RMS level.   In any case, when you convert between dB and W (power, or squared sample values), the multiplier...

  That is why the DR rating is based on the loudest (in terms of RMS level) 20% of blocks. If at least 20% of a track is brickwalled, then it will basically ignore the rest, and report only the dynamic range of the compressed parts.

  For matching the loudness of tracks, it is best to use ReplayGain, as it was designed specifically for this purpose. The relative increase in power needed to play the quiet track as loud as the loud one without clipping can then be calculated from the ratio of the peak levels after ReplayGain...

  Actually, you would need to subtract 3.01 from the dB value, rather than divide it by sqrt(2), so it is 6.9 - 3.01 = 3.89 dB. However, the overall RMS level of this track seems to be in fact -6.9 dBFS referenced to a full scale sine wave, and the peak is obviously 0 dBFS as it is clipped, so...

  Your laptop may already have optical S/PDIF output. It is just often shared with one of the 1/8" TRS connectors to save space.