In this paper, three approaches for estimating ECG derived respiratory signal (EDR) were utilized for apnoea detection and the results were compared with apnoea detection by chest respiratory signals. Two methods are presented for computing the EDR signal by principal component analysis (PCA) applied to entire overnight ECG signals. The proposed approaches simplified the PCA computation and resulted in fast algorithms with low memory requirements. The third method used the QRS area method of EDR estimation. In the first phase, the 8 recordings available in the MIT PhysioNet Apnea-ECG database which contained simultaneously recorded respiratory signals were utilized and the chest respiratory signals were employed for OSA detection and the results were compared to OSA detection by EDR signals. In the second phase, the EDR signals of the 35 available ECG recordings from the same database were used for apnoea detection. The results of both phases for the EDR and respiratory signals were classified by three different machine learning techniques including the extreme learning machine, linear discriminant analysis and support vector machine. It was revealed that QRS area method with LDA classifier results in the highest performance. However, the respiratory signal leads to better apnoea detection compared to the EDR signals.