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Digital data acquisition in experiments

A digital experiment usually measures a continuous physical quantity through a chain rather than converting the phenomenon directly into numbers.

A typical data-acquisition chain is $$\text{physical system}\rightarrow\text{sensor}\rightarrow\text{signal conditioning}\rightarrow\text{sampling}\rightarrow\text{ADC}\rightarrow\text{stored data}.$$ Each stage can limit what the final dataset means.

The sensor has finite sensitivity and bandwidth. Signal conditioning may amplify, filter or shift its output into a range suitable for conversion. Before sampling, frequencies above the usable Nyquist band should be sufficiently suppressed; otherwise they can alias into lower frequencies and cannot be removed afterward from the sampled record.

The analog-to-digital converter samples the conditioned voltage and maps it onto discrete amplitude codes. If an ADC spans a range $V_{\rm FS}$ with $N$ bits, its ideal code width is approximately $$\Delta V=\frac{V_{\rm FS}}{2^N}.$$ Using more bits reduces ideal quantization step size, but it does not eliminate sensor noise, calibration error, limited analog bandwidth or reference-voltage instability.

The sampling rate also determines time resolution. A high sampling rate cannot recover dynamics already attenuated by a slow sensor, while a fast sensor does not prevent aliasing if the digitizer samples too slowly.

Experimental metadata should therefore record not only numerical samples but the measurement chain: sensor calibration, gains, filters, sampling rate, ADC range and relevant timing information.

A digital dataset is the output of a physical instrument model. Interpreting it correctly requires tracing limitations and uncertainty backward through the whole acquisition chain rather than treating stored numbers as direct observations of nature.