Dynamic Range: How Quiet is Quiet?



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References

[Note: This article was originally published in the Widescreen Review Magazine]Most people think of dynamic range as how loud something is. Mathematically though, dynamic range is a ratio. It is the loudest signal divided by “root mean squared” (essentially average) value of noise in the system expressed in decibels. Therefore the dynamic range is reduced if the noise floor of the system is increased. The purpose of this article is to investigate this lower limit.Before diving deep let’s cover some basics. Movie soundtracks come in digital form on the Blu-ray disc. The format supports up to 24 bits of resolution per audio sample. Roughly speaking in digital systems we have 6 dB of dynamic range per sample bit. So 24 bits give us the often mentioned 144 dB of dynamic range. That is a theoretical value. In real life the system without any input will produce fair amount of noise. Due to this factor we lose about 4 bits of our 24 bit sample resolution to noise even in the best digital to analog converters (DACs). This yields an effective sample resolution of 20 bits and dynamic range of 120 dB.In addition to DAC noise, for both live recordings and playback environments we need to consider the noise level that exists in the room. Whatever noise exists there is additive to the equipment noise. To get a sense for that noise floor, let’s run an experiment. If you have a dedicated theater or listening space and a SPL meter, go in there and close the door. Turn on the meter with nothing playing. Likely you see a number in the 50 or even 60 dB range. Taking our original 144 dB and ignoring equipment noise and subtracting this range of values from it, we now have an effective dynamic range of 84 dB to 94 dB. Since the dynamic range of 16 bit audio is 96 dB, it seems that we wasted disc space for 24 bit resolution on our Blu-ray Disc. Indeed the effective range expressed in bits is just 14 bits at the low range of that scale!If you then argue that you are not going to play at 144 dB and knock off 10 to 20 dB due to that, our need for dynamic range shrinks another 2 to 3 bits to paltry 12 to 14 bits. Turn the volume down even more and next thing you know, you can convince yourself that we could go back to cassette tapes and still have sufficient dynamic range for our movies! Indeed there are people who argue exactly this, and conclude then that fidelity differences in our digital gear do not matter as the requirements are for so little resolution. Are they right? Is there a flaw in this analysis? Well, there is. The answer lies in psychoacoustics or how we hear.We start with some of earliest research into how our hearing system works, namely, the Fletcher-Munson equal loudness graphs (see right). The chart is called equal loudness graphs because that is what the lines represent. The numbers on the graph are the loudness level perceived at 1 KHz in dB (SPL) with units of “phon.” As we see for example on the 40 phon line, to get the same 40 dB SPL perceived loudness level at 1 KHz, we would need to boost our 100 Hz signal by a whopping 20 dB! Our hearing is that much less sensitive at 100 Hz relative to 1 KHz. Similar thing happens as frequencies climb above 5 KHz or so.For the purposes of this article we are concerned with the bottom line which is labeled “threshold.” As the name implies, this is the threshold of hearing. Anything below that is considered inaudible (for the average population). That line dramatically shows the “non-linear” response that the ear has. Using 1 KHz as a reference level the sensitivity at 3 KHz actually dips to a negative SPL value as the ear becomes hyper sensitive relative to the rest of the range. At the other extreme of 20 Hz, the threshold is an amazing 70 dB higher for the same level of loudness!Given such high variability one realizes the fallacy of using a single number to describe how noisy a room is. At different frequencies, the minimum audible noise level changes. Hence we cannot use the single number given to use by the SPL meter to compute the dynamic range.To get there we need to decompose the room noise into its frequency components and then compare it frequency to frequency to the threshold line. Only then do we know which ones peak above the threshold and hence are audible. Alas, this is not an easy exercise. The Fletcher-Munson graphs were generated by testing the audibility of test tones. In our application we are instead worried about audibility of noise. Noise is composed of many different frequencies combined so how the ear perceives it is not the same as that single tone. As a result these two numbers cannot be directly compared to each other. Fortunately there is a path there using work done by Bob Stuart (from the Meridian fame) as published in his Audio Engineering Society papers (see reference at the end of the article). It goes beyond the scope of this article to explain how he does that. But suffice it to say, using a variation of above graph known as Equivalent Rectangular Bandwidth (ERB) and some math, we can arrive at comparable values of test tones for each range of noise frequencies.Louis Fielder, working for Dolby and former president of Audio Engineering Society, used Bob’s work to evaluate the entire playback and recording chain from equipment to listening spaces with respect to best dynamic range which can be achieved (see reference at the end of the article). Let’s review the measurements he took with respect to noise floor for a sampling of live halls and a film recording studio:Ah, how fortuitous! The venue noise floor is high at low frequencies where our ears are least sensitive. This means that despite the noise reaching nearly 50 dB SPL, to our ears, the rooms are essentially silent relative to sensitivity of our ears at each frequency. The Skywalker Scoring Stage has especially good performance with nice margin below our threshold of hearing.If you are wondering why the noise level goes up at low frequencies, the simple answer is that they are very hard to block. When you stand outside of your theater, it is the bass frequencies that leak out even if you have significant amount of sound isolation. Likewise, penetrations can occur in reverse direction and let external sound into the room. What might be there may include freeway vibrations from miles away! Extreme low frequency finds a way in. Heating and cooling systems are a week point as by definition they connect a noisy source (motors) to the listening space. For this reason, the above spaces were measured with these units turned off which is accepted practice for recording sessions.Getting professional spaces this quiet with high budgets is one thing but how about home listening spaces? Fielder and his co-author Cohen surveyed 10 homes in one study, and another 27 in a second round and summarized the results in this graph:As with professional spaces, we see elevated noise floors in low frequencies which no doubt fool our simple SPL meters and give us the high values we see on them. The average room is noisier than threshold of hearing but it seems possible to build rooms that are essentially silent as the minimum or the best performing room shows.Fielder shows measurements in his paper for the other extreme for how loud music passages can get in live venues, registering values as high as 130 dB SPL. Using 0 dB SPL as our noise floor then for the quietest rooms we can build, that number translates into the same value of 130 dB number for dynamic range. This means we are simply limited by the DAC dynamic range of 120 dB, giving us 20 bits of effective dynamic range.So it turns out we need high resolution audio (i.e. > 16 bits) after all if we want to make sure our distribution channel, i.e. recorded digital samples, does not add more noise than the rest of the chain. No cassette decks may apply.By the way, much of this was probably intuitively obvious as you noticed how quiet your room was despite the high SPL numbers shown on the meter. As Dr. Toole, one of the top experts in acoustics and speaker design is fond of saying, “two ears and a brain are much more analytical than a microphone and a meter!” Indeed, your ears told the truth better than the measurement device.Stuart, J. Robert, JAES Volume 42 Issue 3 pp. 124-140; March 1994Fielder, Louis D., JAES Volume 43 Issue 5 pp. 322-339; May 1995