  We develop and evaluate two novel purpose-built deep learning (DL) models for
synthesis of the arterial blood pressure (ABP) waveform in a cuff-less manner,
using a single-site photoplethysmography (PPG) signal. We train and evaluate
our DL models on the data of 209 subjects from the public UCI dataset on
cuff-less blood pressure (CLBP) estimation. Our transformer model consists of
an encoder-decoder pair that incorporates positional encoding, multi-head
attention, layer normalization, and dropout techniques for ABP waveform
synthesis. Secondly, under our frequency-domain (FD) learning approach, we
first obtain the discrete cosine transform (DCT) coefficients of the PPG and
ABP signals, and then learn a linear/non-linear (L/NL) regression between them.
The transformer model (FD L/NL model) synthesizes the ABP waveform with a mean
absolute error (MAE) of 3.01 (4.23). Further, the synthesis of ABP waveform
also allows us to estimate the systolic blood pressure (SBP) and diastolic
blood pressure (DBP) values. To this end, the transformer model reports an MAE
of 3.77 mmHg and 2.69 mmHg, for SBP and DBP, respectively. On the other hand,
the FD L/NL method reports an MAE of 4.37 mmHg and 3.91 mmHg, for SBP and DBP,
respectively. Both methods fulfill the AAMI criterion. As for the BHS
criterion, our transformer model (FD L/NL regression model) achieves grade A
(grade B).
