Meteorological Instrument Performance Characteristics

Dynamic Response » Response to Specific Input Functions » Principle of Superposition

First-order and second-order responses are described by ordinary differential equations (ODEs). ODEs are linear in the dynamic sense, but that does not necessarily imply linearity in the static sense. The static sensitivity may not be constant over the range of the sensor, that is, the sensitivity may be nonlinear without a constant slope but the sensor could still be described by a linear ODE. Therefore, the Principle of Superposition applies, meaning that the response of a sensor is the sum of the response of the individual inputs to the device (Brock and Richardson, 2001). This additive property is important and enables the Principle of Superposition to be applied to the frequency decomposition of complex signals by superimposing the responses to individual frequencies.

The Principle of Superposition can be illustrated by considering that the input signal produced by a time-varying measurand can be decomposed into individual sinusoidally-varying signals.

Similarly, individual discrete sources can each produce input signals that add linearly, resulting in a combined input signal that appears to be complex.

An illustration of the Principle of Superposition. The original measurand signal is shown in the bottom-right with the individual decomposed signals as sinusoidal waves and the spectral analysis (energy or energy density) along the frequency axis.