September 2018

Sound System Performance, Part 3
Some effects of signal-to-noise ratio and reverberation.
Article By Peter Mapp, PhD, FASA, FAEs
Article reprinted from Sound & Communications, July 2018

  I am often asked, "How loud does a sound system need to be?" or, more precisely, "What signal-to-noise ratio is required for a system to be intelligible?" The answer, as with most things in audio, is, "It depends."

First, as I have said before, intelligibility is not a black-and-white issue, but, rather, extends over a range, varying from bad / poor to excellent. A number of rules of thumb or industry fall-backs are frequently quoted, with 6dBA or 10dBA signal-to-noise ratio probably being the most common, but 15dBA and 25dBA also often being mentioned. This is a huge range, and it's approximately equivalent to a 100-fold increase in amplifier power! So, what could be considered the minimum and reasonable signal-to-noise-ratio requirements?

The easiest way to determine this is in terms of the Sound Transmission Index (STI), as many system specifications and standards employ this method to assess the potential intelligibility of a sound system. Signal-to-noise ratio (SNR), in terms of STI, at least, is a nominally linear process, with a 3dB increase bringing about a notional improvement of 0.1 STI. I say "nominally linear" because this also depends on the absolute SPL and, to a certain extent, also depends on the spectrum shape of the interfering noise.

You will recall that, last month, I showed that STI is SPL dependent, and this factor must also be taken into account when considering SNR. The graphs presented here are going to take some studying, as I am about to blow some misconceptions and myths out of the water — and probably blow several minds, as well!

Figure 1: STI as a function of SNR for two different SPLs.

Let's begin by looking at Figure 1. Here, I have plotted the effect of SNR on STI for two different scenarios. (Note that the curves are not quite as smooth as theory would predict, as this is real data!)

From Figure 1, it can be seen that, up to around 9dB to 10dB SNR, both curves track each other and follow a linear path. However, at higher SNR values, the curves diverge and, for any given SNR, two different STI values can be obtained. For example, at 18dB SNR, values of 0.79 and 0.84 STI are plotted and, at 24dB, the values are 0.76 and 0.90, respectively.

Whoa, Peter!, I hear you saying. Slow down and explain what is happening here. Surely, SNR is SNR, so isn't it reasonable to expect the same SNR to produce the same intelligibility / STI value? Furthermore, how is it that an improved SNR results in a lower STI value, as is the case at 27dB on the lower curve?

Surely, you are fooling us! (Maybe I should have reserved this article for the April issue....) And not only that, but why aren't the curves straight lines, given that we've said SNR is a linear parameter? These are certainly reasonable comments, and many would think the same thing. (I said I would blow some minds!). OK... now let's get to the bottom of this. Although SNR is an important factor, the absolute SPL must also be considered, and, in fact, it can overrule the SNR effect.

This is what happened here. The upper red curve started off with a nominal signal level of around 60dBA (57dBA, actually, as I also plotted the effect of -3dB SNR). And, so, at +27dB SNR, it reached a level of 87dBA absolute SPL. Now, if you recall the effect that SPL has on STI from last month, you will remember that the SPL intelligibility penalty kicks in at around 83dBA; so, only the last two SNR data points have been affected.

Figure 2: STI as a function of SNR with total SPL also plotted.

However, for the lower blue curve, I started the measurement at 70dBA and, so, the overall SPL reaches 97dBA at 27dB SNR; hence, the overall STI that is achievable is limited and, indeed, it actually begins to decrease as the SPL increases. Figure 2 plots the STI as a function of SNR (blue curve) together with the corresponding overall SPL (green curve).

So, now we can see that you, indeed, can have different STI values for the same SNR!

Figure 1 also clearly demonstrates the way in which SNR affects STI. So, for example, in this particular case, we can see that SNR of 6dBA results in an STI value of 0.58, and 10dBA SNR produces an STI value of around 0.7. So, does this answer the question, "What SNR / SPL is needed?" In a word, "No!" These are not absolute/transferable values — not only in terms of SPL, but also with regard to the STI value, which is very much dependent on the spectrum of the interfering noise. Furthermore, these curves are only valid for an anechoic or completely reflection-free space. (More on that later.)

Figure 3: Effect of different interference noise spectra on STIPA as a function of SNR.

As I noted earlier, the STI for a given SNR is dependent on the spectrum of the background/interfering noise. Figure 3 gives a flavor of that. Here, I have plotted the measured STI versus SNR for four different noise spectra.

Figure 4: Interference noise spectra (all set to 60dBA SPL).

The point to remember is that, at 0dB SNR, all the noise sources and the STIPA signal each individually measured 60dBA (within <0.5dB). This can be seen in Figure 4, which shows the spectra and relative octave band levels of the interfering noises. I employed a wide range of spectrum shapes, as Figure 4 shows, with both high- and low-frequency peaks being present. As Figure 3 shows, although all the measurements were made within the linear range of STI (STIPA, in this case), the resulting plots of STI versus SNR are not particularly linear. This would appear to be a quirk of using "A"-weighted sound levels to set the 0dB SNR SPLs.

Figure 5: Effect of different room acoustic conditions on STI as a function of SNR.

So far, I have only looked at the anechoic or "free field" case. Figure 5 shows the effect of adding four different room acoustic conditions to the situation. Under ideal or noiseless conditions, the average STI values were 0.65, 0.55, 0.51 and 0.47. For this scenario, I used pink noise as the interfering noise, as it is a known entity and reasonably represents a range of conditions (as shown in Figure 3). The curves make interesting viewing, and the truncating function of the STI algorithm can be readily seen kicking in above about 12dBA SNR.

Figure 6: Effect of different room acoustic conditions on STI as a function of SNR with the free-field condition also shown for reference.

Another crucial factor the figure shows is that, even at 15dBA SNR, none of the setups achieves its maximum attainable STI. For example, 0.65 reduces to 0.54; the 0.55 condition reduces to 0.46; 0.51 reduces to 0.44; and 0.47 reduces to 0.40. This has some interesting implications. For example, if you are trying to achieve a criterion of 0.50 STI, Figure 5 shows that a value of 0.55 measured (or predicted) under quiet conditions will not achieve 0.50 STI even with 15dBA SNR. For comparison purposes, Figure 6 also shows the STI / SNR curve measured under free-field conditions (upper dotted curve).

Now, perhaps you can see why I started this article with the question, "What signal-to-noise ratio is required for a system to be intelligible?" The answer is still very much, "It depends!"

About The Author
Technical Council member Peter Mapp, PhD, FASA, FAES, Principal of UK-based Peter Mapp Associates, is a chartered engineer and physicist, and Fellow of the ASA and AES. Mapp was named the 2009 NSCA University Educator of the Year and received the IEC 1906 award in recognition for his work on intelligibility standards and research. He received the AES bronze medal in 2014 in recognition of his significant contributions. Contact him at pmapp@testa.com.

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