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Total Harmonic Distortion (THD): Is It a Good Indicator of Sound Quality?

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Harmonic distortion is often stated as a measurement called Total Harmonic Distortion, or THD, which is a percentage of the overall signal composed of harmonic distortion. THD is not a good indicator of how audible harmonic distortion will be unless it is of an extremely high or extremely low value. This is because there could be relatively high amounts of harmonic distortion in lower orders which could compose a substantial percentage of the output but not enough to surpass masking thresholds and so is inaudible, or there could be only be small amounts of higher order harmonic distortion which lay beyond the range of the masking, and while it may only compose a small percentage of the output, it could easily be audible. In order to determine the audibility of harmonic distortion, we need to see the component harmonics, not just the overall percentage of harmonic distortion. If we can see that the harmonics are either loud enough or of a high enough order that they will lay outside of the masked region for the fundamental, we then know that harmonic distortion will be audible. Let’s take a look at some of the specific examples of this which were observed by Fielder and Benjamin in their study in Table 2, which represents the maximum allowable distortion limits for the 2nd through 5th component harmonics before they became audible:

Table 2.jpg  

Table 2. Reprinted by permission of the AES. 

One obvious and expected trend to see is that lower harmonics are masked much more than higher harmonics, and this, of course, is because they are much closer to the fundamental. Moreover, as was discussed, higher sound pressure levels broaden the masking levels with respect to lower loudness levels, so more harmonics are masked as a percentage at loud levels. However, there is a curious feature of this data set that is worth noting.

One oddity is that at the louder tones of 100 dB and 110 dB, the lower frequencies are better at masking high order harmonics than the higher frequency tones, but not the lower frequency harmonics. For example, at 110 dB, a 20 Hz tone will mask a 2nd harmonic up to 5% of the total output and a 100 Hz tone will mask a 2nd harmonic for up to 2.5%, but for the same loudness level, a 20 Hz tone will only mask a 5th harmonic up to 0.4% while the 100 Hz tone masks the 5th harmonic up to 0.9%. This is counterintuitive to what one would expect from viewing a equal loudness chart, as the steeper slope of human sensitivity at deep frequencies would seem to indicate that further harmonics would be especially audible. This effect is due to the fact that the measured harmonic bands of the lower frequencies are much narrower than the higher frequencies; the 5th harmonic of 10 Hz and 20 Hz is to 50 Hz and 100 Hz respectively, while for 50 Hz and 100 Hz it goes to 250 Hz and 500 Hz. However the masking band of frequencies below 300 Hz remains constant due to a characteristic in our hearing known as critical bands.

Very simply put, critical bands are the bandwidth around a frequency that become activated by that frequency in the human auditory system, and this neural activation causes the perception and sensing of frequencies near the center frequency to interfere with each other. It is a major factor in auditory masking, and the way critical bands act throughout the frequency spectrum of audible sounds changes, so critical bands affect bass frequencies differently than higher frequencies. Below around 200 Hz to 300 Hz, critical bandwidth is roughly a 100 Hz wide band around the center frequency. This means that higher order harmonics of extremely deep frequencies have a better chance of being masked than mid and upper bass frequencies, as their major harmonics are contained within a much closer band to the fundamental.

A More Sensible Metric of Distortion

We have established that THD is a poor measurement to gauge the audibility of harmonic distortion, but now we have a newer and more sophisticated metric that attempts to rate the severity of distortion in bass. CEA-2010 measures the harmonic distortion components of a series of low frequency tone bursts and takes into account the greater audibility of higher order harmonics by weighing them more heavily. CEA-2010 specifies that testing must take place in a controlled environment that has a low ambient noise level, no interfering acoustics, and a limited range of temperature and relative humidity. The tones are played at progressively higher levels until the device will not get any louder or the output distortion of the device crosses a predetermined percentage threshold with respect to the input signal. The highest output level of the tone before crossing the passing distortion threshold is recorded, or, if it didn’t cross the distortion threshold, simply the highest output level is recorded.             

Let’s walk through an example of an iteration of one of the CEA-2010 tone tests to get a closer look at how and why their distortion thresholds were chosen. CEA uses shaped burst tones, and their standard test frequencies are 20 Hz, 25 Hz, 31.5 Hz, 40 Hz, 50 Hz, and 63 Hz. However, the distortion threshold is the same for all of them and therefore can be used to test frequencies above and below those six frequencies. The shape of the input signal can be seen in this 20 Hz burst tone in figure 9; the sound output wave will ideally be an exact match of that electric wave. That is impossible, of course, and our priority should be acceptable distortion, not perfection, hence the use of passing distortion thresholds and not zero distortion.

Tone.jpg  

Fig. 9. 20 Hz CEA-2010 shaped burst tone. Used with permission of Don Keele and Harman International from a CEA-2010 presentation given by Keele in Oct. 2008

The distortion thresholds for CEA-2010 are pictured in Figure 10. The horizontal axis is arranged by harmonic orders, and the test signal is the first harmonic, the fundamental. The stepped lines in the chart indicate the distortion thresholds; in order to achieve a passing CEA-2010 measurement, the output must not generate any harmonics greater than those thresholds. You can see that higher order harmonics have a much lowering passing threshold compared to lower order harmonics, and, as was explained earlier via the equal loudness contour, this is because it is much easier for us to hear higher frequency sounds than deep bass sound, and so sound from those higher harmonic distortions can be audibly objectionable in much smaller amounts.

Figure 10 CEA Distortion Thresholds.jpg

Fig. 10. CEA-2010 distortion threshold for harmonics. Used with permission of Don Keele and Harman International from a CEA-2010 presentation given by Keele in Oct. 2008 

Let’s see how our perfect 20 Hz input signal from Figure 9 would look like against these thresholds in Figure 11:

Figure 11 CEA Burst Tone Spectrum.jpg 

Fig. 11: 20 Hz input signal vs. CEA thresholds. Used with permission of Don Keele and Harman International from a CEA-2010 presentation given by Keele in Oct. 2008 

Unsurprisingly, a perfect signal begets a perfect passing measurement. No harmonic distortion is present in the input signal, of course, and we only show this to demonstrate what a perfect measurement is supposed to look like.

Now let’s see what a real world subwoofer measurement at 20 Hz looks like: the output signal in Figure 12 and its spectra in Figure 13.

Figure 12 CEA Output Measurement.jpg

Fig. 12. recorded 20 hz output CEA-2010 measurement. Used with permission of Don Keele and Harman International from a CEA-2010 presentation given by Keele in Oct. 2008

Figure 13 CEA Measured Output Spectrum.jpg

Fig. 13: spectrum output of 20 Hz CEA-2010 tone. Used with permission of Don Keele and Harman International from a CEA-2010 presentation given by Keele in Oct. 2008.

The changes from the input to the output are very clear. The recorded signal in Figure 12 looks like Figure 9 has been put through the wringer, and, in a sense, it has. It is a recording of the subwoofer run near the edge of its performance, and the mechanical stress is taking a toll on the fidelity of playback. However, if we look at Figure 13, we see that it managed a passing measurement- but just barely, as the third order harmonic distortion was very close to the distortion threshold. The subwoofer recorded this measurement at 103.1 dB.

According to CEA-2010, the output recorded in Figures 12 and 13 is an acceptable level of distortion for a 20 Hz signal. However, when we compare what we see in Figure 13 against the maximum allowable harmonic distortion levels in Table 2 for 20 Hz around the same output level, we see that what is reflected in the CEA-2010 thresholds is well over the limits as established by Fielder and Benjamin’s research. From their findings, a 3rd harmonic that is -15 dB from a 103.1 dB fundamental would be very audible, and they found that for 100 dB and 110 dB, a 3rd harmonic would be heard at -38 dB and -36 dB respectively. CEA-2010 would seem to permit 100 times the amount of distortion than what was found to be audible.

CEA Distortion Thresholds

So why does CEA-2010 permit such high levels of distortion to give a subwoofer a passing grade? There are several reasons. We have to remember that Fielding and Benjamin’s work was done in carefully controlled laboratory conditions. Typical listening conditions will have a lot more background noise and could raise the level of distortion audibility. Another reason is that the test tones used by Fielding and Benjamin and CEA-2010 testing are nothing like normal recorded content people listen to. Normal music and speech is vastly more complex than a single tone at a single amplitude level. Distortion is much more heavily masked in regular content than in pure tones, and the more spectrally complex the content, the more difficult it is to detect distortion. If you have a sound composed of thousands of different frequencies instead of just one, attempting to discern what amount of which frequency is distortion becomes much more difficult.

One element of the human auditory system that lowers the perception of distortion in normal audio content is the fact that human hearing needs time to resolve the frequency spectra of sound. Experiments have shown that it takes 10 to 20 milliseconds to form an opinion on the spectral content of a mid frequency tone and 40 to 60 milliseconds for a low frequency tone. This affects our sensitivity to harmonic distortion, as the shorter the duration of time a sound lasts, the more difficult it is to distinguish what we are hearing. As an example, one study found that it took a 10% level of distortion for listeners to perceive distortion in a 4 millisecond tone. However, when that tone was lengthened to 20 milliseconds, the perceptible level of distortion was lowered to 0.3%. Considering the transient nature of most of the content we typically listen to, this phenomenon is bound to mask far more distortion than what we would hear in more atypical steady state sounds.

One more factor that can make it more difficult to detect distortion is personal familiarity and understanding of the intended reproduction. For example, most people know what a middle C note of a piano is supposed to sound like, but how many people know what a fist fight between two robots from another world is supposed to sound like? Furthermore, the timbre of musical instruments are heavily defined by the harmonic resonances of the instrument’s fundamental, and these resonances typically occur at even order harmonics, which is considered musical since an even order harmonic is always the same note in an upper octave. These even-ordered harmonic resonances of musical instruments can make the detection of even ordered harmonic distortions very difficult, since they are ‘tuned’ to the instrument’s fundamental. On the other hand, this fact makes odd-order harmonic distortion a bit easier to hear since the frequency of that distortion doesn’t cleanly relate to the fundamental, at least in the scale of conventional musical notation. In other words, it’s easier to detect ‘off’ components in a sound we are familiar with. If we have no reference by which to judge the sound, we have no way to know if what we are hearing is apart of the input signal or a distortion in the output. To tie this into the previous discussion, one test showed that even trained listeners were not able to identify as much as 30% distortion peaks from material which had a dense spectra with a high amount of transients and synthesized sounds.

Why Use Test Tones for Distortion Audibility Tests?

testtonesSo if test tones are so removed from ordinary listening content, why use them to test the audibility of distortion? One reason is they are simply the worst case scenario for audible distortion as far as content goes, and if your transducer can perform well in worst-case-scenario conditions then they are much more likely to handle more complex “audibly forgiving” content that much better, so one can think of such testing as “sound quality insurance.” There is media content approaching the simplicity of simple sine waves, although there isn’t much of it. The speaker or subwoofer that can accurately reproduce that content demonstrates a higher performance ability than those that cannot.

Another reason single frequency tones are used for sound quality testing is because they are an easy and well-established way to test speakers. The testing procedure is very simple, easily duplicated and the results are easy and clear to read. One problem with testing with ‘real world’ content, such as movies or speech, is that determining the test content would be extremely difficult, as there are all kinds of criteria by which to determine what should be used as the test signal. Also, one would need a computer with sophisticated software to analyze the results, unlike the clarity of the resulting spectra that a single tone produces.

There are metrics that have been formed to assess distortion which have demonstrated a better correlation of human perception to audible distortion such as the GedLee Metric and the Rnonlin Metric. These methods try to reconcile the modern understanding of psychoacoustics with objective measurements to produce measurements which indicate the severity and audibility of distortion to human perception. However, they are somewhat complicated and have not achieved popular use in the audio industry. It should be noted that any metric that can measure the perceptibility of distortion must necessarily be complicated, as it is measuring the interactions of several immensely complex systems: the physics of sound, the physiological structure of the ear and auditory system, and the psychological processing of the brain.   

 

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Recent Forum Posts:

User5910 posts on August 28, 2015 17:50
This is an excellent, informative post. Thanks!
highfigh posts on August 25, 2015 18:19
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 12:04
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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