Abstarct: Compressed Sensing or Compressive Sampling (CS) is an emerging technique for acquiring and compressing a digital signal with potential benefits in many applications. The method of CS takes advantage of a signal’s sparseness in a particular domain to significantly reduce the number of samples needed to reconstruct the signal. Generally, it requires far fewer samples than Nyquist sampling. One of CS applications is to compress biological signals such as electrocardiogram (ECG) and electroencephalogram (EEG). In this thesis a frxamework for extracting fetal QRS complexes from non-invasive fetal ECG signals is investigated. In the proposed frxamework we used K-SVD dictionary learning and a measurement matrix optimization method to compressively sense ECG signals. We apply Independent Component Analysis (ICA) technique directly on compressed signals to separate fetal and maternal ECG signals and only fetal ECG compressed components need to be reconstructed. Validation of proposed frxamework has been done on Physionet synthetic and real datasets. On dataset A, the frxamework achieves 78.33% mean sensitivity and 67.32% mean positive predictivity with compression ratio of 25%. Comparing with applying ICA on original signals to extract fetal QRS complexes, the proposed method has promising results.