Human Activity Recognition (HAR) is an emerging technology with several applications in surveillance, security, and healthcare sectors. Noninvasive HAR systems based on Wi-Fi Channel State Information (CSI) signals can be developed leveraging the quick growth of ubiquitous Wi-Fi technologies, and the correlation between CSI dynamics and body motions. In this paper, we propose Principal Component-based Wavelet Convolutional Neural Network (or PCWCNN) -- a novel approach that offers robustness and efficiency for practical real-time applications. Our proposed method incorporates two efficient preprocessing algorithms -- the Principal Component Analysis (PCA) and the Discrete Wavelet Transform (DWT). We employ an adaptive activity segmentation algorithm that is accurate and computationally light. Additionally, we used the Wavelet CNN for classification, which is a deep convolutional network analogous to the well-studied ResNet and DenseNet networks. We empirically show that our proposed PCWCNN model performs very well on a real dataset, outperforming existing approaches.