Appropriate blood pressure (BP) management through continuous monitoring and rapid diagnosis helps to take preventive care against cardiovascular diseases (CVD). As hypertension is one of the leading causes of CVDs, keeping hypertension under control by a timely screening of subjects becomes lifesaving. This work proposes estimating BP from motion artifact-affected photoplethysmography signals (PPG) by applying signal processing techniques in realtime. This paper proposes a deep neural network-based methodology to accurately classify PPG signals using a Fourier theory-based time-frequency (TF) spectrogram. This work uses the Fourier decomposition method (FDM) to transform a PPG signal into a TF spectrogram. In the proposed work, the last three layers of the pre-trained deep neural network, namely, GoogleNet, DenseNet, and AlexNet, are modified and then used to classify the PPG signal into normotension, pre-hypertension, and hypertension. The proposed framework is trained and tested using the MIMIC-III and PPG-BP databases using five-fold training and testing. Out of the three deep neural networks, the proposed framework with the DenseNet-201 network performs best, with a test accuracy of 96.5%. The proposed work uses FDM to compute the TF spectrogram to accurately separate the motion artifacts and noise components from a noise-corrupted PPG signal. Capturing more frequency components that contain more information from PPG signals makes the deep neural networks extract better and more meaningful features. Thus, training a deep neural network model with clean PPG signal features improves the generalized capability of a BP classification model when tested in realtime.