Alright. Here is my attempt. Below are from Serge's AES convention paper retrieved from SoundExpert.org. The Df metric is basically computed from the Pearson correlation coefficient ρ(x,y) of the samples of 2 time aligned signals, with Df = sqrt( 1 - abs( ρ(x,y) ) )
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import pearsonr
def dB(x):
return 20.0*np.log10(np.abs(x) + 5.0*np.finfo(float).eps)
def Df(x, y):
return dB(np.sqrt(1.0 - np.abs(pearsonr(x, y).correlation)))
duration = 0.4
fs = 96000
nsamples = int(duration * fs)
t = np.arange(nsamples) / fs
clk_error_list = np.array([1e-4, 1e-5, 1e-6, 1e-7])
frequencies = np.logspace(np.log10(20), np.log10(20480), 201)
df_list = np.empty((np.size(clk_error_list), np.size(frequencies)))
for indx1, clock_error in enumerate(clk_error_list):
for indx2, f_sig in enumerate(frequencies):
signal_1 = np.sin(2*np.pi*f_sig * t)
signal_2 = np.sin(2*np.pi*(1.0+clock_error)*f_sig * t)
df_list[indx1, indx2] = Df(signal_1, signal_2)
fig, ax = plt.subplots(figsize=(8, 5))
for indx, clock_error in enumerate(clk_error_list):
ax.semilogx(frequencies, df_list[indx, :], label='{:.2f} PPM'.format(1e6*clock_error))
ax.grid(True, which='both', axis='both')
ax.legend(loc='upper left')
ax.set_title('Df of Single Frequency Sine Waves Reproduced with Clock Error\n(Sample Duration 400 ms, Fs=96000 Hz)')
ax.set_xlabel('Sine Wave Frequency [Hz]')
ax.set_ylabel('Df [dB]')
fig.tight_layout()
plt.savefig('df_plot.png')
plt.show()
DF Metric is already computed by DeltaWave and has been for years, so it's fairly easy to compare it to other error values computed by DW, including to PK Metric.
Yes, the ADC is also a part but if the same one is used for all tests it can be said to reach at least -80dB so that should be O.K.
The most specific underlying property which is isolated by df-metric (and is not defined/detected by the ones established for 20-30 years+) is the level of overall transparency of a device. Above a certain level of transparency an audio device can be bought without listening it as its artifact/sound signature is reliably imperceptible for human hearing. Such level of transparency can be easily set and measured within df-metric (this will be the topic for another article/paper).
Can you put up the white noise files so we can compare them in DeltaWave?
The ratings from the Df metric look to me like a random number generator.
For example, the Sony NWA105 got a median Df of -71.4 dB and the E1DA 9038 got -42.2 dB.
View attachment 313108View attachment 313109
And here are Amir's measurements. Noise alone in the Sony is much worse than the E1DA. The Df numbers made no sense to me.
The “efficient resampling method” was developed. The time warping algo does it with any predefined accuracy. For example White Noise can be shrinked/stretched with df=-100dB accuracy in the current version. So, the origin of the time inconsistency in #9038 is not the time warping algo.
No need to wonder
DF metric is much more like the RMS of the null value than PK Metric, in that it doesn't use any psychoacoustics in the computation, but instead, computes a short time correlation coefficient between two waveforms (similar to the difference, but a different, and less obvious computation). It's rather an engineering metric based on the whole, unweighted frequency spectrum, just like the RMS null is. For this reason, phase differences, low or high frequency differences, DC filters, etc. can all affect the result of both, DF-metric and the RMS of null.
PK Metric is a psychoacoustically-weighted version of the difference (null) file that is taking into account equal loudness curves at various levels, and frequency and level masking. DF metric does no such thing. After conversations with Serge here and on other fora, I have not seen any explanation for why this metric might be appropriate or better than any other, including the RMS of null file.
We will provide all used/required signals for verification of the results.
RMS of null difference is just as valid as a threshold of transparency measure as df-metric, and perhaps is easier to understand as it is simply the RMS of the difference signal computed by subtracting the original and the recorded waveforms.
That's quite a difference in number. Seeing that PK metric is weighted it makes more sense as to how audible it is.
The null-difference has one disadvantage - it depends on the level of a reference signal. Df is a ratio of the null RMS to the level of reference signal. So, Df is a relative parameter and has exactly the same physical meaning as simple RMS of null difference.Well, I wouldn't say it's "the difference between df-metric and all others"
