I'll bite. However, I will say that I have no professional experience with audio performance evaluation.
So here are the issues I see with the dynamic range comparison of LP to digital.
- RMS calculations are used as a metric for equalized loudness, which I think is not correct. Signals must be passed through an equal-loudness filter of some sort, or at least A-weighting, to evaluate if they are equally "loud".
- The algorithms used for calculating virtually all of the numbers are not broken down, which makes it difficult to impossible for another person to replicate the results. RMS window sizes are not broken down. FFT window sizes are not broken down. FFT window functions are not broken down.
- In general, Mrs. Tham is not actually comparing the dynamic range of LP vs the digital formats, she is merely comparing the dynamic range of recordings of various albums that are released in different formats. As she notes, this introduces many unknowns (the quality of the records, different mastering choices, compression, etc) that compromise the strength of her results. Moreover, this grossly underestimates the actual, numeric dynamic range of CDs. Well, actually, it underestimates the dynamic range of all the formats.
- Comparing peaks of time-domain waveforms is technically misleading and any results based on the comparisons, in my opinion, are not meaningful. They might be corrupted by: phase distortion in the RIAA filter, phase distortion in the reverse RIAA filter during laquer cutting. harmonic distortion on recording or playback, mistracking, and record damage. Again, there are just too many unknowns that can't be factored out.
- The single-number RMS figures Mrs. Tham gives include the energy contributions from rumble, which, as she points out, would grossly favor digital formats in a numerical comparison. Since these recordings are mainly for technical analysis rather than listening, a high-order IIR highpass filter at 50hz or so on both the digital and LP recordings would eliminate all rumble and facilitate more even measurements.
To actually test the real performance of each medium, I think there's no choice but to use test records. One can be constructed easily enough for CD. For LP, the Hi-Fi News test record is servicable, although HFS75 or STR151 (or most CBS test records for that matter) would also work.
I'll admit that Mrs. Tham's test sequence as it currently stands is a lot more "real world" insofar as it uses real music material rather than artificial tones. But I would argue that, when entering a topic as technical as dynamic range in the first place, using music material to measure it is meaningless. You absolutely must use test material specifically designed to measure it.
What we're looking for here is a test tone, at a known calibrated physical amplitude, which can be compared against the average background noise of the recording on a frequency-dependent basis. This ratio forms a signal-to-noise ratio. If the tone is believe to be at or near the maximum amplitude supported by the medium, then it also becomes the dynamic range. (The SNR of vinyl is much less than its dynamic range, due to headroom restrictions. The dynamic range of a digital format is usually the same as its SNR.)
Next, simply using a single RMS number for a signal is not sufficient for evaluating dynamic range, because of the varying effects of harmonic distortion compared to the RMS energy at any single frequency. What I believe is correct is to compare the peak RMS amplitude at a tone's fundamental against the average RMS amplitude of a range of noise frequencies.
Finally, using an excessively long FFT window length will
reduce the accuracy of the LP measurements, not improve it. Because of speed variations in LP playback, if you use a FFT with a high enough frequency resolution, the test tone will move back and forth on the FFT, reducing the tonal energy at any one frequency, while leaving the noise energy undisturbed. This could reduce the measured dynamic range drastically. To get optimal results you need to use a window length that is insensitive to 1-2% of speed variation. For the 300hz tones on HFNRR the window length should be absoutely below 14000 points, and 2048 points is probably close to optimal.
To improve the resolution and consistency of the FFT results you'd need to average all the FFTs together. I'm not sure if CoolEdit will do this.
So, to put it all together, here's a test sequence:
- Grab the Hi-Fi News and Record Review test record, or, failing that, HFS75 or STR151, or, failing that, STR100. (Change the directions below as appropriate.)
- Create a test tone at the highest resolution possible (192/24, or 96/24) for a 30-second, 300hz tone at 0dbFS. Downsample it to 16/44 at the highest quality possible - noise shaped dither, max quality resampling algorithms, etc. Create a test CD with a 30-second track, at 300hz, at 0dbFS maximum amplitude.
- Record the outer band, 300hz, +15db track on side 2 of HFNRR. Trim it to contain only the full-signal tone and no silence. Record it at 44.1khz - not 96khz - because your ADC will invariably run at lower noise at 44.1 than at 96 (unless you know otherwise). Use 24-bit or 32-bit recording.
- Record the test CD track. Trim it. Also record at 44.1/24.
- Run FFTs on every 2048 points of each track. Use a windowing function designed for high dynamic range, but also doesn't have a flat spectral leakage response asymptotically. This means: good choices are Nuttall, Blackman, Hann; bad choices are Rectangular, Hamming, Hann, Gauss, Bartlett, Blackman-Nuttall, and Flat Top.
- Square the FFTs.
- Average the FFTs together.
- Normalize the FFTs so that the 300hz tone has a maximum at 0db. Read out the amplitude at all other frequencies to obtain your frequency-dependent dynamic range readings (but obviously ignore the measurements at harmonics of 300hz). To convert the LP measurements to SNR instead of dynamic range, subtract 15db.