Monitoring of respiratory activity in human beings is very important under many clinical situations. The conventional cumbersome devices, used in recording the respiratory signals, might interfere with the natural breathing of the subject. This book introduces basics of respiratory signal recording, its clinical uses, and problems with direct recording methods. The book presents various signal processing methods for extracting respiratory activity from other most commonly recorded biomedical signals such as Photoplethysmogram (PPG) and Electrocardiogram (ECG). Various signal processing algorithms such as Independent Component Analysis (ICA), Order Reduced Modified Co-variance Auto-regressive (ORMCAR) Modelling, Empirical Mode Decomposition (EMD), Modified Multi-scale Principal Component Analysis (MSPCA) and the Improved Bi-variate Auto-regressive (IB-VAR) modelling are developed for the extraction of respiratory information of the subject from PPG and ECG signals.