## 3 Proposed Method
### Deep Learning Architecture  
To generate systolic and diastolic estimates correlated with the PPG signal, this study explores a deep neural network approach, utilizing feature extraction through vector dimension convolution techniques [36]. Convolutional layers in neural networks mimic the functionality of the Fourier transform, enabling the automatic extraction of frequency characteristics in multiple dimensions. This allows each dimension to capture the most representative values of the highlighted data.  
As seen in Equation (2), convolution is a type of correlation between two functions, \(f\) and \(g\), as one function \"traverses\" over the other shifted around the \(y\)-axis. Convolution is used in machine learning as a means to apply custom filters, which are automatically derived from the training data and function as feature extractors [37].  
\[f(x)*g(x)=\int_{\infty}^{\infty}f(\tau)g(x-\tau)d\tau \tag{2}\]  
Within this approach, the dilation technique was incorporated into the model, thus giving it the ability to store characteristics over time in spatial subsamples related to convolutional layers. This dilation mechanism proves valuable by expanding the receptive field without significantly increasing computational costs [38]. In dilated convolution, filters are applied to areas larger than their lengths, skipping values according to their dilation step. This behavior enables a dilated convolutional network to operate on larger scales compared with a regular convolutional network, achieving a similar effect through pooling or strides (the steps that the filter takes to traverse the receptive field).  
This causes dimensionality reduction as data go from layer to layer in the neural network. Figure 3 illustrates the behavior of this network, highlighting the impact of dilations D1, D2, D4, and D8. These dilations lead to the generation of an output (S), which is intricately connected to a block featuring respective convolutional layers.  
The dilation process unfolds in the following manner: Within a convolutional block, layers are structured with neuron spacings determined by the assigned dilation level. For example, dilation D1 exhibits a spacing of 1 between its neurons. Subsequently, the data extracted by D1 (level 0) are also processed by D2 (level 1), introducing sparser information extraction with a neuron step of 2. The subsequent level, D4 (level 2), carries a dilation of 4, resulting in a spacing of 4 between neurons. This progression continues until reaching the S output layer. The exponential behavior of dilation is repeated for the other dilation levels, fostering the extraction of diverse features within the block's output for the regression of systolic and diastolic points.  
The neural model employed in the proposed method is depicted in Figure 3 and consists of following layers: 4 blocks with dilations mechanisms of 8, 6, 4, and 4, accompanied by corresponding receptive filters of 32, 32, 64, and 64; maximum pooling over vector kernels of length 2; normalization; spatial dropout of 50%; global max pooling; and dense layers with 1 neuron in the output.  
The dilation block, prior to the global max pooling layer, is connected to the composite feature map extraction layers presented at the top of the image. The output of the neural model consists of two dense neurons with linear output for prediction purposes. NeuBP involves a total of 246,690 final parameters.