THD+N measurement with AES17-2015 notch filter

[RJA4000]

Hello

On the newest releases, REW added a "Use AES17-2015 standard notch" checkbox.

This was done, once again, to try and mimic Audio Precision results as close as possible
(In a similar attempt, they added Dolph-Chebyshev 200 windowing. You did as weel: Thanks for that !)

This hardly makes a difference in normal meausrements.
But when using a hardware notch filter to retrieve the very last tenths of DB SINAD on very performant DAC, this has a big impact.

Is that something we could achieve with MI ?
Do I just need a FCF file for this ?
Or do you need to change THD+N is computed for that notch result specifically ?

[VirtinsTech]

Thanks for the information.

According to REW's manual, "...if the 'Use AES17-2015 standard notch' option is selected the fundamental power for THD and THD+N calculations will be the power within a one octave span around the fundamental frequency. If that option is not selected it will be the power in the main lobe of the fundamental. When the fundamental level approaches the noise floor using the standard notch will produce a much higher figure than the fundamental main lobe, in those cases it is better not to use the standard notch...".

It does not seem to be good to use this option for the following reasons:

1. Octave bands do not have a fixed bandwidth. They become wider as frequency increases. In contrast, the main lobes of the fundamental and harmonics do have a fixed bandwidth for a fixed FFT size (The bandwidth is reduced as the FFT size increases). Their widths do not change with frequency. In THD calculation, it is obviously "unfair" if only the fundamental power is calculated based on one octave span around it while the harmonic powers are still calculated based on the main lobe bandwidths. On the other hand, it is also not correct if the harmonic powers are calculated based on one octave span around them because the octave span will be too wide at high frequencies (see table below).

1-1_OctaveBands.png (27.88 KiB) Viewed 93 times

2. It is quite understandable to use this option in THD+N calculation to mimic the hardware method, however, in THD+N vs Frequency measurement, the fundamental frequency will be stepped from 20Hz to 20kHz. Imaging how wide one octave span will be at 20kHz. Even in THD+N @1kHz measurement, one octave span would be from 707Hz to 1414Hz, which is very wide compared with the main lobe method. The noise power inside that range will all be treated falsely as the power of the fundamental.

Having said the above, in Multi-Instrument, it is possible to calculate THD+N with AES17-2015 notch filter like REW using "Energy in user defined frequency bands" function as follows:

1. Define two frequency bands, one for the total energy, the other for the fundamental energy, e.g. 20Hz~20kHz, 707Hz~1414Hz

1.png (25.34 KiB) Viewed 93 times

2. Define a UDDP using the following formula to calculate THD+N:
10*log10(pow(10,[fBand1RMS_A(EU)]/10)-pow(10,[fBand2RMS_A(EU)]/10))/pow(10,[fBand1RMS_A(EU)]/10)
That is: 10*log10([energy in band1] - [energy in band2])/[energy in band1])

2.png (16 KiB) Viewed 93 times

The following picture shows an example of THD+N measurement. The THD+N measured by the AES17-2015 notch filter method is -82.75 dB while -82.58 dB is measured by the normal method. The former is lower because the bandwidth of the notch filter at the fundamental is much wider and the resulting fundamental power contains the contribution from noises in that octave band.

3.png (125.39 KiB) Viewed 93 times

[RJA4000]

Big thanks for your time answering this !

Actually, I was conducting some investigations myself and also found a way to achieve the same:
Using "Energy in Band", I was able to compute D+N Level and "SINAD with AES-17 Notch)
(both on the bottom line)

D+N = 10*LOG10((10^([fBand1RMS_A(EU)]/10)+10^([fBand3RMS_A(EU)]/10)))
and SINAD = -(10*LOG10((10^([fBand1RMS_A(EU)]/10)+10^([fBand3RMS_A(EU)]/10)))-[fBand4RMS_A(EU)])

2022-06-27 12_36_12-Greenshot.png (215.12 KiB) Viewed 87 times

I then get the exact same value than REW.
Problem is that I then loose all other informations regarding Harmonci levels and so on...


This way of working is only important because while using a notch filter, followed by an amp and a compensation file to remove its effect, the "Skirt" is wider, and therefore we have more of the fundamental in the noise than just due to the window lobes.
But that's the only way to get this level of THD+N measurements...

That's a workaround, in my opinion, that was probably introduced by AES standard in 2015 to allow this (especially for Audio Presision hardware, which is using this kind of technique)
So having both options would be great.
Ideally, adding a few additional DDPs for this method ("SINAD AES-17", "SNR AES-17", or so)

Any idea how to solve it ?

[RJA4000]

By the way, I posted this

https://www.audiosciencereview.com/foru ... st-1230502

I hope I didn't write anything stupid...

[VirtinsTech]

This way of working is only important because while using a notch filter, followed by an amp and a compensation file to remove its effect, the "Skirt" is wider, and therefore we have more of the fundamental in the noise than just due to the window lobes.
But that's the only way to get this level of THD+N measurements...

If a proper window function is chosen, the loss of fundamental energy due to the limited calculation bandwidth (BTW, MI has its own way to calculate this bandwidth, somewhat similar to but not exactly as the main lobe method) can be ignored, as illustrated in the following example.

FundamentalBandwidth.png (72.74 KiB) Viewed 66 times

In the above example, the total energy calculated from 0Hz~24kHz is 707.10678679663386 mV (RMS), the fundamental energy f1RMS_A calculated by MI is 707.10678679663374 mV (RMS) which is the same as the energy calculated from 999Hz ~1001Hz. The leakage energy is thus only 0.0000130271 mV (RMS). If the leakage energy is treated as noise and distortion, then the THD+N would be -155dB (from 0~24kHz). The THD+N calculated in the above screenshot is -149.86 dB (from 20Hz~20kHz). This example shows that the leakage of the fundamental by the normal THD+N calculation method can hardly affect any actual THD+N measurement (which is usually much higher than -150dB). On the other hand, with the narrow fundamental energy calculation bandwidth (<2Hz here) compared with the AES17-2015 notch filter (707Hz~1414Hz), much more noise energy is separated from the fundamental energy, resulting in improved measurement accuracy.

[VirtinsTech]

By the way, I posted this...

Thanks for the posting. BTW, the fundamental energy calculation bandwidth increases as FFT size decreases. In case the fundamental skirt is wide due to any reasons, reduce the FFT size.