Лабораторная 2.2 — Aliasing sweep¶

Цель¶

Понять, как тоны выше Nyquist складываются обратно в наблюдаемую полосу и почему без модели aliasing нельзя корректно интерпретировать спектр.

Что выполняется¶

В работе студент:

задаёт реальный sampler с Fs = 1.0 MHz;
строит alias map для широкого диапазона входных частот;
сравнивает спектры для тонов ниже и выше Nyquist;
проверяет measured alias frequency против аналитического расчёта.

Результат¶

После выполнения работы должны быть получены:

карта aliasing input -> observed;
примерные спектры для трёх тестовых тонов;
metrics JSON с expected alias и max alias error;
вывод о требованиях к anti-alias filtering или выбору Fs.

Что приложить к отчёту¶

значение Fs и Nyquist frequency;
график lab22_aliasing_map.png;
график lab22_aliasing_examples.png;
таблицу expected vs measured alias frequencies;
инженерный вывод о том, как избежать неправильной частотной интерпретации.

Подробная техническая часть¶

Lab 2.2 — Aliasing Sweep¶

Goal¶

Show how real-valued sampling folds tones above Nyquist back into the observable band and why aliasing must be predicted before interpreting a spectrum.

Why this matters¶

If a tone above Fs/2 is sampled without adequate filtering, the observed spectrum contains an alias rather than the original RF tone. Without an aliasing model, a measured peak can be assigned to the wrong source.

Experiment¶

The script uses:

sample rate Fs = 1.0 MHz;
a real-valued sampler model;
example tones at 180 kHz, 620 kHz and 1.18 MHz.

It produces:

an aliasing map from 0 to 2.5 * Fs;
example spectra for the three test tones;
measured vs expected alias frequencies.

Run¶

From the repository root:

python blocks/block_02_signals_and_sampling/python/aliasing_sweep.py

Or run the representative lab pack:

python tools/run_all_labs.py

Expected artifacts¶

Artifact	Meaning
`docs/assets/lab22_aliasing_map.png`	mapping from input tone to observed alias magnitude
`docs/assets/lab22_aliasing_examples.png`	spectra for tones below and above Nyquist
`docs/assets/lab22_aliasing_metrics.json`	expected aliases, measured aliases and max alias error

Interpretation checks¶

The 180 kHz tone should appear close to its original frequency because it is below Nyquist.
The 620 kHz tone should fold to approximately 380 kHz.
The 1.18 MHz tone should fold to approximately 180 kHz.
The metrics JSON should confirm that measured alias frequencies follow the analytical alias model within a small error.

Report checklist¶

[ ] Record Fs and the Nyquist frequency.
[ ] Explain why the lab uses a real-valued tone model.
[ ] Attach the aliasing map and the example spectra.
[ ] Compare measured aliases against analytical expectations.
[ ] State what anti-alias filtering or sample-rate change would prevent the wrong interpretation.