Digital signals can be “mixed” or “blended” by using digital summing. This process involves adding two or more signals together using element-wise indexing.

The first sample of one signal is added to the first sample of another signal. The result represents the first sample of the output signal. This process is repeated for the second sample, and all subsequent samples in the signal. For the signals, $x = \{ {x}_{1},{x}_{2},\hdots,{x}_{n} \}$ and $w = \{ {w}_{1},{w}_{2},\hdots,{w}_{n} \}$, the sum of the signals is:

$y = \{ {x}_{1} + {w}_{1},{x}_{2} + {w}_{2}, \hdots,{x}_{n} + {w}_{n} \}$.

The end result is a single signal comprised of both original signals. This process is similar to the task an analog mixing console performs.

Audio engineers sometimes debate whether various digital audio workstations (DAWs) sound different. One question that comes up is whether DAWs perform signal summing using different methods. Unless it is a specific feature of the DAW to use another method, it is almost certainly the case that signal summing is accomplished using element-wise addition in most DAWs.

Next, let’s look at a variation of the summing concept – subtracting signals.