RateConverter — Automatic Cascade Selection¶
What you're seeing¶
Five panels share the same x-axis — normalised frequency in cycles/sample (−0.5 to +0.5 = one full output Nyquist interval).
Top panel — input. 4096 samples of broadband complex noise with a single complex tone injected at fn = 0.04 (4 % of the input sample rate). This is the identical signal fed to all four converters below.
Lower four panels — decimated output, one per cascade topology. Each x-axis is normalised to the converter's output sample rate, so the same physical tone moves to a higher normalised frequency as the rate ratio decreases. The yellow label in the top-left corner of each panel names the exact stages RateConverter selected automatically for that rate.
| Panel | rate | D = 1/rate | Cascade selected | Tone at fn_out |
|---|---|---|---|---|
| HB | 0.5 | 2 | HalfbandDecimator | 0.08 |
| HB×2 | 0.25 | 4 | HalfbandDecimator → HalfbandDecimator | 0.16 |
| CIC | 0.125 | 8 | CIC(8) | 0.32 |
| CIC+Resamp | 0.1 | 10 | CIC(8) → Resampler(0.8) | 0.40 |
Every panel annotates the predicted tone position (fn_out = fn_in / rate) with a green marker. Tone recovery is accurate to well under one FFT bin.
How it works¶
The selection rule is pure arithmetic on D = 1/rate:
rate >= 1.0 or D < 2 → Resampler(rate)
D ≈ 2^1 → HalfbandDecimator
D ≈ 2^2 → HalfbandDecimator → HalfbandDecimator
D = 2^n, n>=3, D<=4096 → CIC(D)
D >= 8, non-power-of-2 → CIC(R*) → Resampler(R*/D)
otherwise (2 ≤ D < 8) → Resampler(rate)
where R* = nearest power-of-two to D. Halfband stages are the cheapest (one multiply per two input samples); CIC has no multiplies at all. The polyphase Resampler handles any rate but is the most compute-intensive, so it is used only when a pure-power-of-two topology cannot be applied.
from doppler.resample import RateConverter
import numpy as np
rc = RateConverter(0.1)
print(rc.stages) # ['CIC(8)', 'Resampler(0.8)']
x = np.random.randn(4096).astype(np.complex64)
y = rc.execute(x) # len(y) ≈ 410
print(len(y))
# Change rate — cascade is rebuilt automatically
rc.rate = 0.25
print(rc.stages) # ['HalfbandDecimator', 'HalfbandDecimator']
The execute buffer is grown lazily on the first call and invalidated on every rate change, so callers pay no per-call allocation overhead in steady state.
See
doppler.resample.RateConverter
for the full API reference.