Time-frequency and preprocessing

Range-Doppler processing assumes target Doppler is nearly stationary over one coherent processing interval. Micro-motion violates that assumption in useful ways: rotating wheels, limbs, and vibration create time-varying Doppler. The short-time Fourier transform (STFT) estimates a local spectrum,

\[ X(m,f)=\sum_n x[n]w[n-mH]e^{-j2\pi fn/F_s}, \]

where \(w\) is a window and \(H\) is the hop size. Smaller segments improve time localization; longer segments improve Doppler resolution. Overlap changes the sampling of time, not the information bandwidth.

from pyradar import rsp

spectrogram = rsp.micro_doppler_spectrogram(
    slowTimeSignal,
    radar=radar,
    segmentLength=128,
    overlap=112,
    fftSize=512,
    window="hann",
)

power = spectrogram.power
velocity = spectrogram.velocity  # m/s, positive approaching
time = spectrogram.time           # s

pyradar.rsp.stft() is the parameter-only form and returns two-sided frequency coordinates. pyradar.rsp.micro_doppler_spectrogram() derives the slow-time sample rate and velocity coordinate from Radar when supplied.

Zoom FFT

Zero-padding samples a conventional DFT more densely but still computes the entire Nyquist interval. pyradar.rsp.zoom_fft() uses the chirp z-transform to evaluate only a requested frequency interval:

zoom = rsp.zoom_fft(
    adc,
    frequencyRange=(120e3, 180e3),
    sampleRate=radar.sampler.sampleRate,
    fftSize=2048,
    axis=-1,
)

The interval is half-open by default, so adjacent intervals do not duplicate an endpoint. Zoom FFT improves frequency-grid spacing in the selected band; it does not surpass the waveform’s physical range resolution.

Composable preprocessing

remove_static_clutter subtracts the coherent slow-time mean and therefore places a notch at zero Doppler. It should be disabled when stationary targets matter or the coherent interval is too short.

coherent_integrate sums complex samples and preserves phase gain. It requires phase alignment. noncoherent_integrate sums magnitudes or powers and is safer across incoherent channels at the cost of coherent processing gain. These are parameter functions; pipeline defaults remain in ProcessingConfig.