Respiratory impedance spectral estimation issues for digitally created random noise from 0-4 Hz and 4-200 Hz

The authors examine the effects of several signal processing issues on the quality of a Z_rs spectral estimate when using a finite-length random sequence created digitally and passed through a D/A (digital-to-analog) converter. The quality of the estimates was evaluated by comparing the mean of the ensemble averaged runs to the theoretical Z_rs (calculated from models) and estimating the coherence function γ²(f). It is shown that regardless of the SNR or model, the Z_rs estimates are superior and the γ² estimates higher for 10 vs. 5 runs. Though this result was expected, the relative improvement in the mean estimate for 10 runs was substantial for a SNR below 200. Even with averaging 10 runs, however, the Z_rs and γ² estimates were still poor for SNR<100 at frequencies where the magnitude of load impedance (i.e., Z_rs) was high (e.g. 0-1 Hz and 128-160 Hz). At higher Z_rs the local spectral magnitude of the output flow is much lower than the average magnitude of the flow spectrum over all f_k. Consequently the effective local SNR is significantly less. Again, poorer estimates were expected, but the extent of the sensitivity to noise renders the estimate useless for model fitting. Due to wider main lobe of the Hanning window, a spectral estimate at a given frequency can be biased