Estimation of respiratory frequency from Heart Rate Variability - Ågärd,Daniel (Master's Theses in Mathematical Sciences, 2023)
In this master's thesis the ability to estimate the respiratory frequency from heart rate variability measurement is analyzed. The goal was to implement a solution that is easily transferable to real time. Starting from the initial processing of data, continuing with two different spectrogram implementations, a single spectrogram and a multitaper spectrogram, combined with three different methods of spectral estimates for each time step in the two spectrograms, the respiratory frequency is estimated. A relatively limited real data set, in combination with the necessity to evaluate the different permutations of methods in a controlled environment, created the need to start on simulated data. The different permutations of methods were evaluated on the simulated data with sane defaults in order to find the best performing methods. The chosen methods were then applied to real data containing 97 different individuals. In order to maximize the different methods' capabilities the real data was divided into two data sets, one for training, and one for validation, containing 31 and 66 individuals each. The best performing methods found in the simulations were then evaluated with different parameter choices, and the weights for a multitaper spectrogram method were optimized. The conclusion is that the respiratory frequency is possible to estimate with a low margin of error from the traditional high frequency band, $0.12-0.4$Hz, of the heart rate variability. The ever present time-delay of time-frequency estimates when using a spectrogram is the main contributor to the errors when estimating the actual frequency of a signal, when no noise is present. This is also the case when estimating the true respiratory frequency from the heart rate variability. If the minimization of time-delay in the frequency estimate is needed, a standard spectrogram, combined with a high heart rate will maximize the possibility of accurately estimating the respiratory frequency from the heart rate variability. For most applications outside a controlled environment however, the signal-to-noise ratio is a problem. With the small drawback of a few seconds more of extra time-delay, any multitaper spectrogram solution will perform equal or better than a single spectrogram method for time-frequency estimation. If a ''real time'' estimation is of no concern, a simple offset in time in post-processing of the estimated respiratory frequency will yield a result with the best of two worlds.
Keywords: time-frequency analysis; multitaper spectrogram; Optimization; signal processing; heart rate variability