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The extraction of complex axial wavenumbers is a key intermediate step in modal sound-field decomposition and liner impedance eduction. This paper presents a systematic benchmark comparison of the Kumaresan--Tufts (KT) and Hankel total least squares (HTLS) methods for controlled two-dimensional synthetic test cases in lined ducts. The analysis covers single-mode benchmarks for varying SNR, noise model, and microphone array geometry, and is complemented by a compact multimodal stress test based on realistic no-flow SDOF Helmholtz-resonator liner trajectories. In noise-free cases, both methods recover the damped-exponential signal model essentially exactly. Under noisy conditions, the extraction error increases by roughly one decade per $20\,\mathrm{dB}$ reduction in SNR, turbulent boundary-layer noise is slightly more detrimental than white noise at low SNR, and HTLS is globally more robust, particularly for modes with positive imaginary part. The geometry study shows that the dominant array-design parameters are the dimensionless products $k_x \Delta x$ and $k_x l$.