Lab 2.3 — I/Q Interpretation and Mirrored Spectrum¶

Goal¶

Demonstrate the difference between correct complex I/Q capture, swapped I/Q channels, and a real-valued capture that produces mirrored spectra.

Why this matters¶

Complex baseband separates positive and negative frequencies. If the I/Q order is wrong, the spectrum can be mirrored. If only a real-valued channel is used, positive and negative frequency content becomes symmetric and direction information is lost.

Experiment¶

The script builds a complex tone at 120 kHz and compares three cases:

correct complex I/Q;
I/Q swapped by exchanging the real and imaginary parts;
real-valued capture that keeps only the I channel.

The lab measures:

peak position for the correct complex signal;
mirrored peak for the swapped-I/Q case;
positive and negative mirror peaks for the real-valued capture.

Run¶

From the repository root:

python blocks/block_02_signals_and_sampling/python/iq_visualization.py

Or run the representative lab pack:

python tools/run_all_labs.py

Expected artifacts¶

Artifact	Meaning
`docs/assets/lab23_iq_components_time.png`	I/Q components in the time domain
`docs/assets/lab23_iq_interpretation_spectra.png`	correct, swapped and mirrored spectral views
`docs/assets/lab23_iq_metrics.json`	peak locations and mirroring checks

Interpretation checks¶

The correct complex I/Q case should show the main tone near +120 kHz.
The swapped-I/Q case should mirror the tone to the negative side of the spectrum.
The real-valued capture should show matching positive and negative peaks around +/-120 kHz.
The metrics JSON should confirm a small error for the correct case and near-symmetric mirror peaks for the real-valued case.

What to expect¶

Correct peak: 119995.117 Hz
I/Q swapped peak: -119995.117 Hz
Real-valued positive/negative peaks: 119995.117/-119995.117 Hz

Swapping I and Q mirrors the spectrum exactly: +120 kHz becomes -120 kHz. Swapping the two parts turns x into j * conj(x), and conjugation reverses the direction of rotation.
A real-valued capture shows both +120 and -120 kHz with equal height. A real signal cannot tell the two directions apart; this is why an SDR delivers two channels, I and Q.
A mirrored spectrum is the typical symptom of a wrong i_first setting or of a receiver that uses the other sign convention for the LO. Nothing in the samples says which one is right, so it has to be recorded in the metadata and checked with a known tone.

Exercises¶

Conjugate the correct signal (np.conj(x)) instead of swapping I and Q. Compare the peak with the swapped case. Why are they equal?
You record a known FM station that should appear at +300 kHz and it appears at -300 kHz. List two possible causes and one experiment that separates them.
Why does the real-valued capture need twice the sample rate of the complex one to cover the same bandwidth?

Answers (checked by running the lab script)

Swapping I and Q gives Q + jI = j·conj(x): the conjugate multiplied by a constant phase. The magnitude spectrum is the same, so both move the tone to −f at the same level.
Either the I/Q order or the sign of Q is wrong somewhere in the capture or the reader, or the RF chain inverts the spectrum (a mixing stage with the LO above the signal). To separate them, open the same recording in a different program (HDSDR, SDR++): if it shows +300 kHz, your reader is at fault; if every program shows −300 kHz, the inversion happened before the file was written.
A real signal's spectrum is symmetric, X(−f) = X*(f), so the samples carry only 0 to Fs/2 uniquely; a complex signal carries −Fs/2 to +Fs/2. The amount of data is the same: the complex stream has two real numbers per sample.

Report checklist¶

Explain why complex baseband can distinguish spectral direction.
Attach the time-domain I/Q plot and the spectral comparison plot.
Quote the correct, swapped and mirrored peak locations.
Explain what acquisition or parsing mistake produces an I/Q swap in practice.
State how the same issue would appear in a real SDR recording workflow.