LO — Complex Phasor Generator¶

LO chains a 32-bit NCO with a 2¹⁶-entry sin/cos LUT to produce CF32 IQ phasors. freq is a normalized frequency in cycles/sample (0.25 = fs/4).

Free-running tone¶

from doppler.source import LO
import numpy as np

lo = LO(0.25)          # quarter-rate tone
iq = lo.steps(8)

# The float32 LUT leaves ~1e-7 residue on the axes, so compare with a tolerance.
assert np.allclose(iq, np.tile([1, 1j, -1, -1j], 2), atol=1e-6)

CF32 precision

The LUT holds float32 values, so values like 0+1j appear as -8.7e-08+1.000000e+00j in repr(). Its index is the top 16 bits of the phase, truncated, so the phase error is < 2π/2¹⁶ ≈ 9.6 × 10⁻⁵ radians (zero here, where the increment is a whole number of LUT bins). The spurs it makes are ≥ 90 dBc down; ~96 dBc is typical.

FM via control port¶

Per-sample frequency deviation added on top of the base frequency:

ctrl = (0.002 * np.sin(2 * np.pi * 0.01 * np.arange(1024))).astype(np.float32)
lo2 = LO(0.1)
iq = lo2.steps_ctrl(ctrl)

Phase continuity¶

Successive calls resume exactly where the last left off:

lo3 = LO(0.25)
a = lo3.steps(4)   # samples 0–3
b = lo3.steps(4)   # samples 4–7, phase continuous

expected = np.tile([1, 1j, -1, -1j], 2)
assert np.allclose(np.concatenate([a, b]), expected, atol=1e-6)