I explain the "operating window method" below.
Please see the material. → QE15
p.1: The horizontal axis is time, and the vertical axis is the concentration of the reacting substance. As time passes, the concentration of reactants decreases and the concentration of main product (light blue part) increases. The by-products from by- reactions also increase slightly. Ideally, we make a goal that the main product concentration is high and the by-products one are low. I make aim to expand like a yellow arrow. This light blue part is called "functional window". The graph on the right shows the vertical axis as a logarithmic axis. The light blue part is the functional window.
p.2: Suppose you have a spectrum with the horizontal axis representing wavelength and the vertical axis representing light intensity. yn is noise, (Yn-ym) is the desired signal, and ym is the average value of noise. In this case, Sm is the sum of squares of the desired signal, and the SN ratio η1 is the third expression from the top. On the other hand, it is better to have less noise. ST is the sum of squares of noise and VT is its average value. We calculate the SN ratio η2 using the reciprocal of VT. The larger η1 and η2 are better. Since the SN ratio has additivity of factorial effects, the total SN ratio η can be expressed as the sum of η1 and η2. The SN ratio of the functional window on the previous page corresponds to this η. By-products correspond to noise. Main product corresponds to signal.
How is it? Making the noise as low as possible and the signal as high as possible will widen the functional window. This “functional window” is a concept that can be used in various situations.