Spectral Doppler measurements are an important part of the standard echocardiographic examination. These measurements give insight into myocardial motion and blood flow providing clinicians with parameters for diagnostic decision making. Many of these measurements are performed automatically with high accuracy, increasing the efficiency of the diagnostic pipeline. However, full automation is not yet available because the user must manually select which measurement should be performed on each image. In this work, we develop a pipeline based on convolutional neural networks (CNNs) to automatically classify the measurement type from cardiac Doppler scans. We show how the multi-modal information in each spectral Doppler recording can be combined using a meta parameter post-processing mapping scheme and heatmaps to encode coordinate locations. Additionally, we experiment with several architectures to examine the tradeoff between accuracy, speed, and memory usage for resource-constrained environments. Finally, we propose a confidence metric using the values in the last fully connected layer of the network and show that our confidence metric can prevent many misclassifications. Our algorithm enables a fully automatic pipeline from acquisition to Doppler spectrum measurements. We achieve 96% accuracy on a test set drawn from separate clinical sites, indicating that the proposed method is suitable for clinical adoption.