Thanks a lot to
@alvaro-oliver for contributing to the understanding and application of w&f measurements.
If I may, I would like to put some notes on what it really is we want to measure and calculate.
For most of the tools I’ve seen, different ways to calculate wow, flutter and w&f is presented. Does the user really know what’s going on and how to address this? Do they know what is good and what is not good? What to aim for?
Does it get clarified by showing eight different ways to present W/F/W&F? Especially when not showing
how they are calculated?
W&F is defined by two major things;
- how much (how many +/- Hz) the speed deviates from the average speed. These amplitudes are called frequency deviations. Let’s call them Δf.
- how fast the speed moves from and to maximum and minimum deviations. These cycles are called modulation frequencies. Let’s call them fm.
Both the frequency deviation and the modulation frequency is inherent in the
carrier frequency (let's call it µ). Here's an illustration of these three parts of the signal we want to measure (note that the y-axis is Hz, not volts):
Wow is simply defined as fm<6Hz and flutter is fm>6Hz. Frequencies below 0.5Hz is called drift and it’s a different topic. Flutter is normally measured up to less than 100Hz.
In order to measure Δf and fm we use a carrier frequency, which is the average speed of the track (the groove velocity) on a test LP. It’s an old habit to use 3150Hz sine which seems a bit odd, but it’s the midpoint between 1 and 10kHz on a log scale paper. Let’s call the carrier frequency fc.
Music is not pure sine waves but instead a compound of very complex waveforms and transients, so in a similar way as we use rms values and not peak values to denote magnitude of varying levels, it is common to use a value of the deviation Δf which is not exceeded 95% of the time (of a measurement). This is called 2σ (two-sigma) i.e. two standard deviations of a normal (gauss) distribution.
I made a summary illustration;
Our hearing is normally most sensitive to a frequency deviation of 4Hz. So, it is most annoying if a 1kHz tone is meant to be pure but sways between 996 and 1004Hz. If it sways less
or more than that, it is less annoying. Therefore, a weighting factor was expressed in AES6-2008. We can call this factor α.
In my opinion, based on all the above, we should help ourselves in trying to stick to one common nomenclature, e.g. w&f % 2σ weighted AES6-2008 test tone 3150Hz.
If we do that, a sensible requirement based on human perception is then to not exceed w&f +/-0.2% 2σ.
It is very easy to measure a signal for the analysis of speed, wow and flutter. But it is quite complicated to
calculate the W&F. For most disturbances or properties of sound, we can use filters and/or FFT to extract the information. But for W&F we can’t do that because the signal is frequency modulated. The W&F is inherent in the signal. Therefore, again in my opinion, it is important that the tool maker states the method used to calculate the W&F.
To conclude, if we assume the speed deviation has a normal distribution, the following should be measured and calculated for a turntables speed, wow and flutter. τi can be regarded as the individual periods in a measurement (i.e. the inverse of the instantaneous frequency fi):
(the calulation of α is an approximation of the AES6-2008 curve)
The requirements we should put depends of the standard of the player and is in the end up to each of us, but for a good standard turntable I would recommend:
- 33.0 < SPEED < 33.7rpm
- W&F < +/-0.2% 2σ weighted AES6-2008
The test record (and all our LPs) has some warp and the center hole is never perfectly centered. The record player shouldn’t be blamed for that, so 0.55Hz wow (33rpm) should be disregarded or filtered out. The same goes for cart-tonearm resonances usually in the range 8-12Hz.
Please comment/correct if something is misunderstood or unclear.
@alvaro-oliver ; how do you calculate the zero crossings in the sampled signal? I understand you bandpass the signal, but is the band really small enough?
