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Perceptually-Motivated Objective Grading of Nonlinear Processing in Virtual-Bass Systems

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When size limitations of loudspeakers prevent the reproduction of low-frequency sounds, nonlinear devices can be used to create the illusion of the missing bass. Such virtual bass systems generate harmonics of the missing fundamental. However, they also can generate unwanted intermodulation distortion, which appears to be dependent on the particular audio sample and the selected nonlinearity. A detailed analysis showed that the ideal nonlinearity should not be even-symmetric, and its second derivative should be less than zero on the input interval 0 to 1.

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JAES Volume 59 Issue 11 pp. 804-824; November 2011
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Christophe Macours
Comment posted January 27, 2012 @ 16:50:03 UTC (Comment permalink)

Very interesting article.

One question regarding to the bass-intensity listening test: the results in Table 11 show that the equalized track (EQ) scores marginally better than the reference (REF). Can you comment on this?

Can the authors also provide more details on the exact filter specifications (LPF, HPF1, HPF2 and EQ) and the rationale behind those choices?

Many thanks in advance for your feedback.

 


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Nay Oo
Comment posted January 29, 2012 @ 16:30:48 UTC (Comment permalink)

Thank you for your interest and questions.

Question 1: One question regarding to the bass-intensity listening test: the results in Table 11 show that the equalized track (EQ) scores marginally better than the reference (REF). Can you comment on this?


Answer 1: In the bass-intensity listening test, we use high-pass filter 2 (HPF2) (see Fig. 1). For HPF2, the cut-off is 100 Hz (see Section 4.2) to evaluate the virtual-bass effect generated by different NLDs. Equalization was performed off-line using Adobe Audition 2.0 software. The settings are as follows: Effects > Filters > Graphic Equalizer > 20 Bands> 12 dB for {-31, 44, 63, 88, 125, 180, 250} and 0 dB for the rest. The purpose of inclusion of EQ is to show that simply equalizing the low-frequencies does not work when low-frequencies cannot be reproduced due to the physical limitations of transducers (here we use HPF2 to simulate this effect). The listening test results in Table 11 shows the fact that is your question. EQ does not improve bass perception when some physical bass components are removed. Some NLDs due to its harmonic generation and missing fundamental effect can create virtual bass perception on the contrary and can enhance better bass intensity perception than simply equalization.



Question 2: Can the authors also provide more details on the exact filter specifications (LPF, HPF1, HPF2 and EQ) and the rationale behind those choices?

Answer 2: The rationale for including EQ in the experiment has been explained above. We followed Lasen and Aarts structure (Fig. 1 of [1]) to evaluate different NLDs on bass perception and distortion perception. One main difference is that we do not use band-pass filter (BPF)  in both experiments but instead included HPF2 separately in the second experiment, bass intensity listening test. The rationale is to evaluate the distortion artifacts caused by these NLDs in the first experiment without including BPF. The filter specifications of LPF and HPF1 are described in Section 3.3 and 4.2 of our paper.

Reference:
[1] E. Larsen and R. M. Aarts, "Reproducing low-pitched signals through small loudspeakers," J. Audio Eng. Soc., vol. 50, pp. 147-164, 2002.


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Christophe Macours
Comment posted February 3, 2012 @ 16:38:54 UTC (Comment permalink)

Many thanks for your answers. Please find below three additional questions.

Q1) In Aarts's article, HPF2 and LPF have the same cut-off frequency. This is a logical choice, since their intention was to evaluate the added value of the harmonics components on bass perception. In your article, HPF2 and LPF have cut-off frequencies of 100 Hz and 280 Hz respectively. What did motivate the choice of a lower cut-off frequency for HPF2?

Q2) As a result of the cut-off frequency difference reported in Q1, when reproducing your experiment (using the ATSR NLD), I tend to conclude that the bass enhancement mostly results from the gain (around +7 dB) caused by the NLD on the fundamental frequencies present in the band between 100 Hz and 280 Hz, and not much - if at all - from the generated harmonics. Did you come across the same observation?

Q3) Could you also provide more details on filter HPF2? Does it have the same steep roll-off as LPF and HPF1?


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Author Response
Nay Oo
Comment posted February 4, 2012 @ 19:18:08 UTC (Comment permalink)

Thank you again for your interest and questions.

Q1) In Aarts's article, HPF2 and LPF have the same cut-off frequency. This is a logical choice, since their intention was to evaluate the added value of the harmonics components on bass perception. In your article, HPF2 and LPF have cut-off frequencies of 100 Hz and 280 Hz respectively. What did motivate the choice of a lower cut-off frequency for HPF2?

Ans: We used the same cut-off 280 Hz for both LPF and HPF1 (See Fig. 1 (b) and Fig. 5). The purposes of HPF2 in this article and FIL2 in Aart’s article are different. There is no HPF2 in Aart's article. FIL2 is a band-pass filter in Aart’s article to shape harmonic spectrum. We used HPF2 to simulate loudspeaker low-frequency bandwidth limitation problem.

Q2) As a result of the cut-off frequency difference reported in Q1, when reproducing your experiment (using the ATSR NLD), I tend to conclude that the bass enhancement mostly results from the gain (around +7 dB) caused by the NLD on the fundamental frequencies present in the band between 100 Hz and 280 Hz, and not much - if at all - from the generated harmonics. Did you come across the same observation?

Ans: I have explained the difference in filters and their purposes above. The main idea is that instead of shaping harmonic spectrum and removing the physical bass completely using FIL2, we let the physical bass components pass through the audio processing system together with generated harmonics by NLDs but we do not use any band-pass-filter (BPF) after NLD. HPF2 is instead used for simulating loudspeaker low frequency cut-off (See Fig. 1(b)). Not only ATSR, but also NLDs such as EXP2, FEXP1, NTANH and NSIG are good bass enhancers. See Table 14 and Fig. 11.

Q3)
Could you also provide more details on filter HPF2? Does it have the same steep roll-off as LPF and HPF1?

Ans: For the HPF2, before the experiment 2 (i.e., bass intensity listening test), the wave files were high-passed filtered using Adobe Audition 2.0 > Effects > Scientific Filters. The cut-off is 100 Hz and the filter types and roll-off are not the same as LPF and HPF1. Note that HPF2 is not a part of bass enhancement system but is applied here to simulate low-frequency bandwidth limitation problem.

Ref:

E. Larsen and R. M. Aarts, "Reproducing low-pitched signals through small loudspeakers," J. Audio Eng. Soc., vol. 50, pp. 147-164, 2002.


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Christophe Macours
Comment posted February 10, 2012 @ 17:17:22 UTC (Comment permalink)

Thanks again for your answers.

It would have been wise to ensure all NLDs have a unity gain on the physical bass components. That would have helped the assessment of the true virtual bass enhancement, the one resulting from the generated harmonics only without boost of the physical bass components. Indeed, an FFT comparison of the NLDs in terms of fundamental frequency gain yields the following results (from the highest to the lowest gain, sinewave input) :

  1. ATSR: +5.65 dB
  2. EXP2: +5.05 dB
  3. FEXP1: +0.60 dB
  4. NTANH: +0.55 dB
  5. NSIG: +0.15 dB
  1. REF: +0.00 dB
  1. FEXP2: -0.70 dB
  2. SQS: -1.40 dB
  3. CUBE: -2.50 dB
  4. CLP: -4.30 dB
  5. HWR: -6.00 dB
  6. ASQRT: no fundamental
  7. FWR: no fundamental
  8. SQL: no fundamental

Interestingly, the "Good" bass enhancers are precisely those with a positive gain on the fundamental frequency. It seems fair to state that the author's conclusions would have been quite different if all NLDs would have had their fundamental frequency gain normalized to unity, such that they would only have differed by their non-linear behaviour.


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Author Response
Nay Oo
Comment posted February 11, 2012 @ 17:12:44 UTC (Comment permalink)

Thank you again for your interest, research efforts, and comments.

I would like to add on a few things. The physical bass-boasting nature of NLDs is related to the derivative analysis of the nonlinear IO curves. Please see Table 14, Table 15 and Figure 11 of our paper. Your findings indicate that the good NLDs have physical bass boasting effect together with virtual bass effect caused by missing fundamental. Bad NLDs suppress the physical bass or lack of the physical bass. Our derivative analysis of NLD curves in the paper shows the same thing. In my humble opinion, it is not feasible to normalize the physical bass component (i.e., fundamental frequency or first harmonic) without modifying the nonlinear IO curves.

Moreover, bass intensity is only one half of the issue; the other half is the distortion artifacts caused by NLDs and deployment of Rnonlin model [1] to predict the scores.

Ref:
[1] C. T. Tan, Moore, B. C. J., Zacharov, N., and Matilla, V.-V., "Predicting the perceived quality of nonlinearly distorted music and speech signals," J. Audio Eng. Soc., vol. 52, pp. 699-711, 2004.
 


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