The other day, I was discussing signal-to-noise ratio (SNR) with a colleague and bemoaning the fact that many research papers/articles do not define what they mean by this, nor indeed state how the signal and noise levels were actually measured. Knowing the SNR of a broadcast or transmitted signal is of vital importance if you want to know how well it will be heard or, in the case of speech signals, if it will be intelligible. It would seem to be a pretty obvious measure and mundane task to undertake…but is it? As soon as you begin to consider it, a host of variables and possibilities open themselves up for consideration.
As with all things acoustic and audio, there are three domains that we need to consider: Amplitude, Frequency and Time, or AFT, as I sometimes refer to them. If we were to consider the Digital domain, as well, I guess that would be DAFT, but I digress. Back to measuring signals and noise.
Let’s start by considering the Amplitude component. The obvious approach is to measure the amplitude in decibels (dBs). But what sort of dBs? After all, the decibel is a ratio, so we, therefore, have to define the reference. For audio, that could be a voltage, resulting, perhaps, in a measurement in dBv or dBu, with reference levels of 1.0V and 0.775V, respectively. Alternatively, it could be a sound pressure, with a reference of 20 micro Pascals, resulting in dB SPL (Sound Pressure Level).
Equally, it may not always be necessary to define the reference if we are just comparing similar values, although it should normally be stated. For the purposes of our discussion here, I will be using dB SPL (although I will not generally refer to this) because the results and essence of this discussion could also occur in the electronic, rather than acoustic, domain.
So, I am going to measure the signal amplitude and noise in dB. But will these be linear or frequency-weighted dBs? This now brings in the first raft of potential variables. For example, the most common weighting in acoustics, and also in much audio work, is the “A” weighting, thus providing dBA as the measure. Equally, I could choose the “C” weighting, so I could measure the value in dBC.
Alternatively, I could opt for a linear response or no weighting, which is termed dBZ. A few years ago, I could have also opted for a “B” weighting and dBB. (So now you see where the cunningly crafted subhead of “A, B, C to Z” comes from.).
OK. So I have dealt (sort of) with the frequency element “F.” Now all that remains is the Time element “T.” When trying to measure a time-varying signal such as speech (or, indeed, a lot of real-world noise, come to that), you soon realize what an almost impossible task this can be with the meter needle or digital display whizzing around all over the place (see Figure 1). The solution, therefore, is to provide the display with a time constant or integration of the information over a set period of time when displaying the value.
This resulted in the formulation and standardization of “Fast” and “Slow” time weightings (often referred to as “F” and “S”), and even simple sound level meters offer this capability, along with A- and C-weighting filters. When reporting a measurement value, therefore, the weighting and integration time used to make the measurement should be stated. The quick and conventional way to do this is to use the designatory letter (A, C or Z) with the integration time as a subscript. Hence, dBAF denotes an A-weighted fast integration time measurement, and dBCS a C-weighted measurement made with the Slow time constant. These days, the sound levels may also be denoted as LAF and LCS.
In Figure 2, I have plotted the A and C weighting curves because it’s useful to understand what they are actually doing. For good measure (not sure if that pun was intended), I have also thrown in the “B” curve, as well, because some meters and software still provide this and I have found it to be very useful on occasion.
To recap, we now have the following parameters and variables at our disposal when attempting to measure the wanted signal and noise:
- A: decibels with or without a nominal reference
- F: frequency weighting A, C and Z (plus a bunch of others beyond the scope of this discussion)
- T: Fast or Slow integration time
So, we are all set to make a measurement, but which parameters to use, and does it really matter or make a difference? The quick answer to that question is, you bet it does, although the difference will be highly dependent on the type and nature of the signal involved. Typically, for example, there can be a 3dB to 4dB difference between Fast and Slow A-weighted, averaged readings and a 4dB difference between A- and C-weighted values when measuring a typical speech signal.
Depending on the nature of the noise that has to be overcome by a PA system, for example, these differences can vary enormously when measuring the noise level (e.g., by 10dB or more). Therefore, as can be seen, assigning an SNR may not be as straightforward as it may have seemed at first. Comparing and matching speech levels and test signals opens up a whole new can of worms that I will leave for another time.
However, to give a flavor of this, the screenshots shown in Figure 1 give an idea. These are some sound level meter screen snapshots I took when assessing a typical PA system message. As you can see, the Fast response varied from 78.0dBA to 92.5dBA, but was effectively impossible to read because it changed so much and too rapidly; thus, no two users reported the same value. (In fact, I wasn’t aware of some of these values until I looked at the images!). When the meter was set to slow, however, the identical signal was much easier to read.
Although actually varying by 3dB (83.1dB to 86.4dB) the meter visually read ~86dBA and could consistently be read reasonably accurately. However, measuring the LAeq (the equivalent or “average” sound level and the preferred method employed by experienced acousticians and many international standards) was extremely stable, varying by no more than 0.4dB, and everyone making the same measurement could be in agreement to within better than 0.5dBA.