## Socratic Coffee on why particle size matters (Part V: signal-to-noise ratio)

At this point in our series, we’d like to introduce a framework we think is very useful when it comes to brewing and tasting coffee. You might have heard the term “signal-to-noise ratio” (often abbreviated to SNR). With a SNR framework, the world can be thought of as containing stimuli we are interested in (signals) mixed with stimuli we are not interested in (noise). SNR is the ratio of signal power to noise power.

In our last column (December 2016), we mentioned a concept of optimal extraction, where the ratio of extracted compounds from a coffee particle results in the subjectively deemed “tastiest brew”. We can label this tastiest ratio our desired “signal”. Deviations from our target ratio lead to a less desirable or muddled signal — so under or over extraction can be termed “noise”.

Think of it as the amount of static you hear when trying to tune into a radio station. There is an optimal point for the signal – anything more or less introduces an increasing amount of static. Our goal is to shift the SNR in favour of the signal as much as possible (the highest SNR value as possible).

Without getting too technical, it is possible to apply some basic mathematical modelling of SNR in a coffee brew by comparing the average extraction ratio of a particle distribution to the standard deviation of the overall extraction. This would look like this – equation 1 on right.

In this formula, x is the sample’s average extraction ratio and s is the sample’s standard deviation in extraction ratio. Since we know that extraction is linearly correlated with particle size, we can potentially use particle size as a surrogate for extraction ratio and use this to help us determine how uniformly a particular particle distribution will extract. While this is not the only approach and, some may argue, an overly simplistic approach, it does allow us to objectively quantify and compare coffee particle distributions using a single metric.

The main patterns used to describe data’s distribution include the centre of the distribution (such as median or mean), spread (variability of the data), shape (symmetry, number of peaks, skewness, uniformity), and any unusual features (such as gaps, outliers). In coffee, depending on the application, some may argue for unimodal (one peak) distributio ns versus bimodal (two peaks). Let’s take Figure 1 as an example. On left.

To determine our overall average particle size (x) and standard deviation (s), we will follow a standard approach in this second formula: on right.

In this example, x is particle size and p is a calculated value from our distribution representing the percentage of the entire distribution at each particle size. Standard deviation is calculated using this third formula:

From these two formulas, we see that our distribution has an average particle size (x) of 304.75 micrometres with a standard deviation (s) of 88.03 micrometres. Applying these values to our SNR equation mentioned previously, we see a SNR of 3.5.

Now let’s compare that to some other distributions. See Figure 2. The SNR values have been calculated for all distributions. As we might expect from our visual assessment of the distributions, those with taller and sharper peaks tend to have higher SNR values.

By now you’ve heard us say over and over that coffee solubles extract at a very predictable rate.

The full article features in the February 2017 edition of BeanScene Magazine.