Lab 2.1 — Sampling Axis and Interpretation¶

Goal¶

Verify that the same captured signal can produce a correct-looking but incorrect engineering conclusion if the sampling rate is interpreted incorrectly.

Why this matters¶

A spectrum plot is only meaningful together with the correct Fs. If Fs is wrong, every FFT bin is mapped to the wrong physical frequency, even when the plot shape itself still looks plausible.

Experiment¶

The script generates a complex tone with:

correct sample rate Fs = 1.0 MHz;
intentionally wrong interpretation Fs = 0.8 MHz;
non-zero DC offset;
additive noise;
a known expected tone near 123.456 kHz.

The lab compares:

time-domain I/Q preview;
FFT magnitude with the correct frequency axis;
the same FFT magnitude with a wrong frequency axis;
measured peak frequency error for both interpretations.

Run¶

From the repository root:

python blocks/block_02_signals_and_sampling/python/sampling_analysis.py

Or run the representative lab pack:

python tools/run_all_labs.py

Expected artifacts¶

Artifact	Meaning
`docs/assets/lab21_sampling_time_domain.png`	I/Q preview in time domain
`docs/assets/lab21_sampling_frequency_axis.png`	correct vs wrong `Fs` interpretation on the FFT axis
`docs/assets/lab21_sampling_metrics.json`	expected tone, measured peaks and interpretation errors

Interpretation checks¶

The correct interpretation should place the tone close to the expected 123.456 kHz.
The wrong interpretation should shift the measured peak significantly, even though the spectral shape still looks reasonable.
The metrics JSON should show a small error for the correct axis and a much larger error for the wrong axis.
The time-domain preview should also help detect DC offset and clipping risk before moving to frequency-domain conclusions.

Report checklist¶

[ ] Record the assumed Fs, FFT size and tone frequency.
[ ] Explain why the same FFT magnitude can support both a correct and a wrong conclusion.
[ ] Attach the time-domain preview and the frequency-axis comparison plot.
[ ] Quote the correct and wrong frequency errors from the metrics JSON.
[ ] State which metadata field must be protected in a real IQ capture workflow.