μ is mean. It’s calculated as ever:

In electronics, the mean is commonly called the DC (direct current) value. Likewise, AC (alternating current) refers to how the signal fluctuates around the mean value. If the signal is a simple repetitive waveform, such as a sine or square wave, its excursions can be described by its peak-to-peak amplitude.

So basic signals can be analyzed with things like the mean, but most signals are complex. For this, we bring in the standard deviation, denoted by σ. The average deviation is calculated simply, with just summing absolute values of differences from the mean. But the standard deviation squares things, because we’re more interested in signal power - P ∝ V^2 - so we get:

Note the N - 1 in the summation - this is important later.

σ^2 occurs a lot, and is called the variance. Standard deviation is fluctuation from the mean, and variance is the power of this fluctuation. We also have root-mean-square (rms):

By definition, the standard deviation only measures the AC portion of a signal, while the rms value measures both the AC and DC components. If a signal has no DC component, its rms value is identical to its standard deviation.

Often we want to do running statistics of means, standard deviations, variances, etc. without having to recalculate everything from scratch. Additionally, the equations above have rounding / floating-point errors if not careful. An alternate equation helps:

Two more terms:

• signal-to-noise ratio (SNR): mean divided by the standard deviation
• coefficient of variation (CV): standard deviation divided by the mean, multiplied by 100 percent.

Better data means a higher value for the SNR and a lower value for the CV.