Uniform spline interpolation is fully defined by its continuous-domain impulse response. I noticed that the integral of the square of the impulse response over its support gives the average amplification of the power of white noise error in the samples.
What is this figure or its square root called? Is "white noise gain" $(\operatorname{WNG})$ appropriate for the square root?
For example for linear interpolation:
Figure 1. Linear interpolation impulse response
$$\operatorname{WNG} = \sqrt{\int_{-1}^1\left(\left\{\begin{array}x+1&\text{if }x<0\\1-x&\text{otherwise}\end{array}\right.\right)^2dx} = \sqrt{\frac{2}{3}}\approx0.8164965809$$