Time series versus Fourier transform methods for estimation of respiratory impedance spectra

Most current techniques to estimate respiratory system mechanical input impedance spectra (Zrs) use digitally created (Fourier transform (FFT) based) random noise. Recent Zrs data reported from 0.1-4 Hz and above 32 Hz display sharper, more distinct spectral features. When expressing Zrs as a power spectral density (PSD), such features suggest the application of a time series spectral estimation approach. Here, a simulation study was performed to compare the quality of impedance (PSD and Zrs) estimates from the time series technique to those from the FFT approach in the presence of measurement noise. Random noise pressure and flow time domain sequences were simulated for two different networks, one which exhibits impedance features reported from 0.1-4 Hz and one which exhibits impedance features reported above 32 Hz. In the time series method, autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models were fit to the pressure and flow sequences separately. The estimated PSD and complex Zrs spectra were compared to the true spectra calculated from the models. Results show that the time series PSD estimates were reasonable even in the presence of additive measurement noise. Conversely, with additive noise, the time series estimates of the complex Zrs showed a negative real part which is physiologically inappropriate. This occurs because of the loss of phase information inherent to the time series approach. Regardless of measurement noise, the FFT estimates of impedance were always close to the true impedance and always superior to the time series estimates. We conclude that an accurate estimate of the PSD or complex Zrs spectra from digitally created FFT-based random noise is best obtained using the traditional FFT method.