Real-time multi-signal frequency tracking with a bank of notch filters to estimate the respiratory rate from the ECG

Measuring the instantaneous frequency of a signal rapidly and accurately is essential in many applications. However, the instantaneous frequency by definition is a parameter difficult to determine. Fourier-based methods introduce estimation delays as computations are performed in a time-window. Instantaneous methods based on the Hilbert transform lack robustness. State-of-the-art adaptive filters yield accurate estimates, however, with an adaptation delay. In this study we propose an algorithm based on short length-3 FIR notch filters to estimate the instantaneous frequency of a signal at each sample, in a real-time manner and with very low delay. The output powers of a bank of the above-mentioned filters are used in a recursive weighting scheme to estimate the dominant frequency of the input. This scheme has been extended to process multiple inputs containing a common frequency by introducing an additional weighting scheme upon the inputs. The algorithm was tested on synthetic data and then evaluated on real biomedical data, i.e. the estimation of the respiratory rate from the electrocardiogram. It was shown that the proposed method provided more accurate estimates with less delay than those of state-of-the-art methods. By virtue of its simplicity and good performance, the proposed method is a worthy candidate to be used in biomedical applications, for example in health monitoring developments based on portable and automatic devices.