Лабораторная 7.2 — Частотный перенос DUC/DDC

Цель

Промоделировать цифровое повышение и понижение частоты в TX/RX-тракте и проверить, что сигнал оказывается в ожидаемой точке спектра на каждом этапе.

Что выполняется

В работе студент:

1. формирует baseband-сигнал;
2. выполняет DUC-перенос;
3. рассчитывает RF/RX frequency plan;
4. применяет DDC-сдвиг;
5. строит спектры до и после DDC;
6. оценивает остаточную частотную ошибку.

Результат

После выполнения работы должны быть получены:

• графики спектров TX/RX;
• график контрольных частотных точек;
• metrics JSON;
• вывод о корректности знаков DUC/DDC.

Что приложить к отчёту

• TX LO и RX LO;
• TX digital offset;
• DDC shift;
• FFT-графики;
• measured peak и residual frequency error;
• инженерный вывод.

Подробная техническая часть

Lab 7.2 — DUC/DDC Frequency Translation

Goal

Model digital upconversion and downconversion in a TX/RX chain and verify that the target signal moves to the expected frequency at each stage.

The lab answers the practical question:

How do TX digital offset, RF LO frequencies and RX DDC shift determine where the signal appears in the final baseband?

Executable files

Environment	File	Output
Python	blocks/block_07_tx_rx_chains/python/lab_7_2_duc_ddc_frequency_translation.py	FFT figures + metrics JSON in docs/assets

Run from the repository root:

python blocks/block_07_tx_rx_chains/python/lab_7_2_duc_ddc_frequency_translation.py

Generated artifacts:

docs/assets/lab72_duc_ddc_tx_spectrum.png
docs/assets/lab72_duc_ddc_rx_spectrum.png
docs/assets/lab72_duc_ddc_frequency_plan.png
docs/assets/lab72_duc_ddc_metrics.json

Processing chain

flowchart LR
    BB[Baseband tone] --> DUC[DUC mixer]
    DUC --> RFPLAN[RF frequency plan]
    RFPLAN --> RX[Receiver baseband]
    RX --> DDC[DDC mixer]
    DDC --> OUT[Near-DC output]

Frequency equations

TX RF tone:

f_rf = f_tx_lo + f_tx_offset

Receiver observed baseband offset:

f_rx_obs = f_rf - f_rx_lo

After DDC:

f_out = f_rx_obs + f_ddc_shift

Correct DDC choice:

f_ddc_shift = -f_rx_obs

Example

Parameter	Value
TX LO	915 MHz
TX digital offset	+100 kHz
RX LO	915 MHz
RX observed offset	+100 kHz
DDC shift	-100 kHz
Final output offset	0 Hz

Practical procedure

1. Generate a complex tone at baseband.
2. Apply DUC shift.
3. Interpret the result through the RF frequency plan.
4. Generate a receiver IQ signal at the observed offset.
5. Apply DDC shift.
6. Plot FFT before and after DDC.
7. Estimate output peak frequency.
8. Verify that the output peak is close to DC.

Expected plots

• TX baseband spectrum;
• after DUC spectrum;
• RX observed spectrum;
• after DDC spectrum;
• frequency error summary.

Metrics generated by the script

Metric	Meaning
tx_rf_hz	RF frequency implied by TX LO and DUC shift
rx_observed_offset_hz	expected receiver baseband offset
ddc_shift_hz	digital shift applied in RX DDC
rx_peak_hz	measured peak before DDC
final_peak_hz	measured peak after DDC
final_frequency_error_hz	final peak minus expected final frequency
snr_db	rough SNR estimate after DDC

Common sign mistakes

Mistake	Symptom	Fix
DDC sign is wrong	signal moves farther from DC	use negative observed offset
TX/RX LO relation ignored	expected peak is wrong	compute TX_LO + offset - RX_LO
real mixer used instead of complex mixer	image appears	use complex IQ mixing
sample rate mismatch	peak appears at wrong FFT bin	check metadata sample rate
IQ conjugation	spectrum mirrored	check I/Q ordering and sign convention

Report checklist

• [ ] State TX LO and RX LO.
• [ ] State TX digital offset.
• [ ] Compute RX observed offset.
• [ ] Select DDC shift.
• [ ] Plot FFT before DDC.
• [ ] Plot FFT after DDC.
• [ ] Estimate output frequency error.
• [ ] Explain any residual offset.

Engineering conclusion template

The TX/RX frequency plan predicts an RX observed offset of ____ Hz.
Using DDC shift ____ Hz, the final output peak is ____ Hz.
The residual frequency error is ____ Hz and is mainly caused by ______.