Developing accurate classification models for radar-based Human Activity Recognition (HAR), capable of solving real-world problems, depends heavily on the amount of available data. In this paper, we propose a simple, effective, and generalizable data augmentation strategy along with preprocessing for micro-Doppler signatures to enhance recognition performance. By leveraging the decomposition properties of the Discrete Wavelet Transform (DWT), new samples are generated with distinct characteristics that do not overlap with those of the original samples. The micro-Doppler signatures are projected onto the DWT space for the decomposition process using the Haar wavelet. The returned decomposition components are used in different configurations to generate new data. Three new samples are obtained from a single spectrogram, which increases the amount of training data without creating duplicates. Next, the augmented samples are processed using the Sobel filter. This step allows each sample to be expanded into three representations, including the gradient in the x-direction (Dx), y-direction (Dy), and both x- and y-directions (Dxy). These representations are used as input for training a three-input convolutional neural network-long short-term memory support vector machine (CNN-LSTM-SVM) model. We have assessed the feasibility of our solution by evaluating it on three datasets containing micro-Doppler signatures of human activities, including Frequency Modulated Continuous Wave (FMCW) 77 GHz, FMCW 24 GHz, and Impulse Radio Ultra-Wide Band (IR-UWB) 10 GHz datasets. Several experiments have been carried out to evaluate the model's performance with the inclusion of additional samples. The model was trained from scratch only on the augmented samples and tested on the original samples. Our augmentation approach has been thoroughly evaluated using various metrics, including accuracy, precision, recall, and F1-score. The results demonstrate a substantial improvement in the recognition rate and effectively alleviate the overfitting effect. Accuracies of 96.47%, 94.27%, and 98.18% are obtained for the FMCW 77 GHz, FMCW 24 GHz, and IR- UWB 10 GHz datasets, respectively. The findings of the study demonstrate the utility of DWT to enrich micro-Doppler training samples to improve HAR performance. Furthermore, the processing step was found to be efficient in enhancing the classification accuracy, achieving 96.78%, 96.32%, and 100% for the FMCW 77 GHz, FMCW 24 GHz, and IR-UWB 10 GHz datasets, respectively.