This research article presents a novel methodology for effectively extracting the fetal electrocardiogram (FECG) from a single-channel signal acquired on the maternal abdomen. The signal comprises a mixture of the FECG, maternal electrocardiogram (MECG), and ambient noise. The central concept involves projecting the signal into higher-dimensional spaces and leveraging the assumption of statistical independence among the constituent components to achieve their separation from the mixture. To accomplish this, singular value decomposition (SVD) is initially applied to the spectrogram, followed by an iterative application of independent component analysis (ICA) on the principal components. The SVD technique contributes to the enhanced separability of each individual component, while ICA facilitates the promotion of statistical independence between the fetal and maternal ECGs. Furthermore, we refine and customize the aforementioned approach specifically for ECG signals by incorporating knowledge of the frequency distribution of the MECG and other inherent ECG characteristics. The effectiveness of the proposed methodology is validated through comprehensive experimental studies, demonstrating its superior accuracy and performance compared to existing techniques.