Electrocardiogram (ECG) signals, profiling the electrical activities of the heart, are used for a plethora of diagnostic applications. However, ECG systems require multiple leads or channels of signals to capture the complete view of the cardiac system, which limits their application in smartwatches and wearables. In this work, we propose a modally reduced representation learning method for ECG signals that is capable of generating channel-agnostic, unified representations for ECG signals. Through joint optimization of reconstruction and alignment, we ensure that the embeddings of the different channels contain an amalgamation of the overall information across channels while also retaining their specific information. On an independent test dataset, we generated highly correlated channel embeddings from different ECG channels, leading to a moderate approximation of the 12-lead signals from a single-channel embedding. Our generated embeddings can work as strong features for ECG signals for downstream tasks.