A measuring instrument interacts with the system it measures and has its own dynamics. Treating an instrument as an ideal observer can therefore distort both the signal and the system.

An instrument's response function describes how its output depends on the physical input. Static response includes sensitivity, offset, linearity and saturation. Dynamic response describes how quickly the instrument follows changing input. A first-order sensor, for example, may satisfy $$\tau\frac{dy}{dt}+y=Kx,$$ where $x$ is the true input, $y$ the indicated output, $K$ the static gain and $\tau$ the response time. Rapid variations with timescale much shorter than $\tau$ are attenuated.

The corresponding bandwidth describes the range of temporal or frequency variation that can be measured without unacceptable distortion. Measuring a $10,\mathrm{kHz}$ waveform with a sensor whose response rolls off around $1,\mathrm{kHz}$ will not recover the original waveform even if the digital sampling rate is very high.

Loading occurs when attaching the instrument changes the system. A voltmeter with finite input resistance $R_m$ draws current from the circuit it measures. If the measured source can be modeled as an ideal open-circuit voltage $V_0$ in series with source resistance $R_s$, connecting the meter gives $$V=V_0\frac{R_m}{R_s+R_m}.$$ When $R_m\gg R_s$, loading is small; otherwise the measurement itself significantly changes the voltage.

Experimental design therefore asks two separate questions: can the instrument respond to the phenomenon, and does coupling the instrument alter it? Resolution and sampling cannot compensate for inadequate bandwidth, saturation or strong loading.