Doppler echocardiography offers critical insights into cardiac function and phases by quantifying blood flow velocities and evaluating myocardial motion. However, previous methods for automating Doppler analysis, ranging from initial signal processing techniques to advanced deep learning approaches, have been constrained by their reliance on electrocardiogram (ECG) data and their inability to process Doppler views collectively. We introduce a novel unified framework using a convolutional neural network for comprehensive analysis of spectral and tissue Doppler echocardiography images that combines automatic measurements and end-diastole (ED) detection into a singular method. The network automatically recognizes key features across various Doppler views, with novel Doppler shape embedding and anti-aliasing modules enhancing interpretation and ensuring consistent analysis. Empirical results indicate a consistent outperformance in performance metrics, including dice similarity coefficients (DSC) and intersection over union (IoU). The proposed framework demonstrates strong agreement with clinicians in Doppler automatic measurements and competitive performance in ED detection.