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Intermodulation Distortion: Can it Predict Good Bass Performance in Subwoofers?

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One other major nonlinear distortion we will discuss is called intermodulation distortion. Like harmonic distortion, it will be present in all speakers, but at what point does it become audible in bass frequencies?

Before we try to answer that question, let’s define it. As we have seen with harmonic distortion, a single tone can interact with the transducer to produce multiple tones in the output. Intermodulation distortion is when multiple input tones interact with each other in the transducer to produce many more tones in the output. The additional tones generated by intermodulation distortion are not harmonically related to the fundamentals. Instead the distortions are frequencies that are the sum and differences of the fundamentals and the multiples of those sums and differences. This is illustrated in Figures 14a and 14b:

Figure 14a Two Tone Input Signal.jpg

Figure 14a: Two tone input signal

Figure 14b IMD Spectrum.jpg

Fig. 14b. Intermodulation products and their frequency values relative to the fundamentals  

Like harmonic distortion, intermodulation distortion is measured as a percentage, but as with the THD percentage, the percentage of intermodulation distortion may not be very meaningful with respect to audibility. Usually the amount of intermodulation distortion is proportional to the amount of harmonic distortion, with their relative values depending on the ratio of the amplitudes of the test signals. The tones used to test intermodulation distortion will also generate harmonic distortion, and it is possible for a speaker to exhibit low harmonic distortion but still generate high levels of intermodulation distortion. The amount of intermodulation distortion generated depends on the density of the input spectra. As the input signal becomes more complex the intermodulation distortion becomes greater, and this can be seen of a speaker measurement in Figure 15, where hundreds if not thousands of spectral distortion components are generated from a handful of input frequencies in a multi-tone burst.  As with harmonic distortion, those intermodulation products closest in frequency to the fundamental are the most likely to be masked. Unlike harmonic distortion, intermodulation distortion products can be spread further out over the frequency spectrum and therefore may not be masked as well, so intermodulation distortion is potentially more audible than harmonic distortion.

Figure 15 Measured IMD Spectra.jpg 

Fig. 15. Spectrum of multi-tone burst and nonlinear distortion byproducts (a). Reprinted by permission of the AES.

While some studies have shown that human perception is extremely sensitive to intermodulation distortion for much of the spectrum of human hearing, the audibility of intermodulation distortion in low frequencies was thought to be equal or less than that of harmonic distortion by Fielder and Benjamin in their research. Their reasoning was that the intermodulation difference products would be masked by the effects of the critical band in the lowest 100 Hz bandwidth of hearing, which, as we described before, would be dominated by the fundamental in that range. As for the sum intermodulation products, they would be no more audible than the harmonic distortion products by virtue of necessarily being less in amplitude, since the energy of intermodulation distortion is spread out more rather than concentrated in certain frequencies. For these reasons, they did not attempt to run tests on the audibility of intermodulation distortion in low frequencies. Subwoofer reviewer and tester Ilkka Rissanen, who is perhaps the only subwoofer tester to have released IMD measurements of tested subwoofers (seen on this page), commented that subwoofers with low THD levels also had low intermodulation distortion levels. Regarding audibility, he said there were clear audible differences between the best and worst performers from the subwoofers that he tested. 

A Quixotic Quest

If you read this article in the hope of being able to identify exactly when your subwoofer or bass driver is beginning to markedly alter the sound through distortion, you will undoubtedly be disappointed. The only hard numbers that exist for levels at which humans could just begin to detect distortion were reprinted in table 2, and those were only for sine wave tones in a laboratory condition from listening subjects who had healthy hearing. Chances are, your listening environment isn’t quite as controlled, and your choice of listening content is a bit more complex, and, if you are a bit older, your hearing might not be as acute. In other words, those numbers are not the performance targets you should sweat over if you want pristine bass sound quality. Your sense of hearing is likely to tolerate far more distortion before you would ever notice than those numbers would indicate. In order to find ‘just detectable levels’ of distortion in normal listening content such as music would require one to be intimately familiar with the recording or be able to switch between a non-distorting version of that recording faster than aural memory can fade, which may be as brief as three to four seconds.

However, this isn’t to say the problem of understanding the thresholds of identifiable distortion in these low frequencies is so intractable that it isn’t worth attempting to solve. Distortion does occur, and it does change the sound from what was originally intended by the artist. By identifying the point at which distortion becomes audible, effort can be more sensibly invested in reducing it there, instead of wasted in reducing it where it is already beyond the limit of human perceptibility.   

References

Ahonen, Jukka, et al. "Perception and physical behavior of loudspeaker nonlinearities at bass frequencies in closed vs. reflex enclosures." Audio Engineering Society Convention 124. Audio Engineering Society, 2008.

Czerwinski E., Voishvillo A., Alexandrov S., and Terekhov A.: Multitone Testing of Sound Systems - Some Results and Conclusions, Part 1: History and Theory, J. Audio Eng. Soc., vol. 49, No. 11, pp. 10111027, (2001, November).

Fielder, Louis D., and Eric M. Benjamin. "Subwoofer performance for accurate reproduction of music." Journal of the Audio Engineering Society 36.6 (1988): 443-456.

Geddes, Earl R., and Lidia W. Lee. Audio Transducers. GedLee, 2002.

Geddes, Earl R., and Lidia W. Lee. "Audibility of linear distortion with variations in sound pressure level and group delay." Audio Engineering Society Convention 121. Audio Engineering Society, 2006.

Gunnarsson, Viktor. Assessment of nonlinearities in loudspeakers: volume dependent equalization. Chalmers University of Technology.

Harwood, H. D. "Loudspeaker Distortion with Low-Frequency Signals." Journal of the Audio Engineering Society 20.9 (1972): 718-728.

J. Moir, "Just Detectable Distortion", Wireless World, vol. 87, no. 1541, Feb. 1981.

Klippel, Wolfgang. "Speaker auralization-Subjective evaluation of nonlinear distortion." PREPRINTS-AUDIO ENGINEERING SOCIETY (2001).

Klippel, Wolfgang. "Nonlinear large-signal behavior of electrodynamic loudspeakers at low frequencies." Journal of the Audio Engineering Society 40.6 (1992): 483-496.

Klippel, Wolfgang. "Loudspeaker Nonlinearities–Causes, Parameters, Symptoms." Audio Engineering Society Convention 119. Audio Engineering Society, 2005.

Klippel, Wolfgang, and Robert Werner. "Loudspeaker Distortion–Measurement and Perception."

Mitchell, Peter W. "The Measure of Bass Quality" Stereo Review, December 1995, pg 144.

de Santis, M. E., and Simon Henin. "Perception & thresholds of nonlinear distortion using complex signals." Section of Acoustics, Institute of Electronic Systems, Aalborg University (2007).

Schmitt, R. Audibility of nonlinear loudspeaker distortion. Journal of the Audio Engineering

Society, 43(11):402, May 1995.

Temme, Steve, et al. "The Correlation between Distortion Audibility and Listener Preference in Headphones." Audio Engineering Society Convention 137. Audio Engineering Society, 2014.

Voishvillo, Alex. "Measurements and Perception of Nonlinear Distortion—Comparing Numbers and Sound Quality." Audio Engineering Society Convention 123. Audio Engineering Society, 2007.

Voishvillo, Alex. "Assessment of Nonlinearity in Transducers and Sound Systems–from THD to Perceptual Models." Audio Engineering Society Convention 121. Audio Engineering Society, 2006.

Voishvillo, Alexander, et al. "Graphing, interpretation, and comparison of results of loudspeaker nonlinear distortion measurements." Journal of the Audio Engineering Society 52.4 (2004): 332-357.

Voishvillo, Alexander, et al  “Measurement of Loudspeaker Large Signal Performance - Comparison of Short-Term Testing Signals”  Audio Engineering Society (2002).

 

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Recent Forum Posts:

User5910 posts on August 28, 2015 18:50
This is an excellent, informative post. Thanks!
highfigh posts on August 25, 2015 19:19
To be clear, this curve set is for the SPL of the sound to be heard with equal intensity, not the ear's sensitivity at those frequencies which, according to that idea, would mean that we're far less sensitive to the 1KHz-5KHz range than we are to the extreme low and high frequencies. Human hearing is more sensitive in the range where this curve shows the dip between 2KHz and 5KHz. According to this link (and the other information they have, human hearing acuity is highest between 3.5KHz and 4KHz.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/maxsens.html

From the text below the last graph, "Where the curve dips between 2000-5000Hz, this implies that less sound intensity is necessary for the ear to perceive the same loudness as a 120dB, 1000Hz tone. In contrast, the strong rise in the curve for 0 phons at low frequencies shows that the ear has a notable discrimination against low frequencies for very soft sounds.". This is the reason loudness controls boost the bass and treble and specific to Yamaha, their variable compensation curve produces more bass and treble at lower levels.

Here's another link-

http://www.extron.com/company/article.aspx?id=loudnesscontrol_ts

I remember curves from past reading that were the inverse of this- not sure why they don't appear with searches, now.
gene posts on August 13, 2015 13:04
Bass is the most physically demanding band for a home theater system to reproduce, so it will naturally be the region where distortion is the most prevalent. Those of us interested in higher fidelity sound would do well to understand the degree of which distortion in low frequencies can be heard and the challenges involved in finding those distortion thresholds. This article discusses those challenges and relays some of the current understanding of the subject from the field of audio science.

Is your sound system up to the task of faithfully reproducing bass content, and if not, how short does it fall between your hearing and the sound engineer’s intention?


Read: The Audibility of Distortion At Bass Frequencies
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