  Despite the population of the noninvasive, economic, comfortable, and
easy-to-install photoplethysmography (PPG), it is still lacking a
mathematically rigorous and stable algorithm which is able to simultaneously
extract from a single-channel PPG signal the instantaneous heart rate (IHR) and
the instantaneous respiratory rate (IRR). In this paper, a novel algorithm
called deppG is provided to tackle this challenge. deppG is composed of two
theoretically solid nonlinear-type time-frequency analyses techniques, the
de-shape short time Fourier transform and the synchrosqueezing transform, which
allows us to extract the instantaneous physiological information from the PPG
signal in a reliable way. To test its performance, in addition to validating
the algorithm by a simulated signal and discussing the meaning of
"instantaneous", the algorithm is applied to two publicly available batch
databases, the Capnobase and the ICASSP 2015 signal processing cup. The former
contains PPG signals relative to spontaneous or controlled breathing in static
patients, and the latter is made up of PPG signals collected from subjects
doing intense physical activities. The accuracies of the estimated IHR and IRR
are compared with the ones obtained by other methods, and represent the
state-of-the-art in this field of research. The results suggest the potential
of deppG to extract instantaneous physiological information from a signal
acquired from widely available wearable devices, even when a subject carries
out intense physical activities.
