A system for monitoring a patient's respiratory rate, comprising: a first sensor selected from the group consisting of: i) an impedance pneumography sensor comprising at least two electrodes and an impedance pneumography processing circuit configured to process signals from the two electrodes to measure an impedance pneumography signal from the patient; ii) an ECG sensor comprising at least two electrodes and an ECG processing circuit configured to process signals from the two electrodes to measure an ECG signal from the patient; and iii) a PPG sensor comprising a light source, photodetector, and PPG processing circuit configured to process signals from the photodetector to measure a PPG signal from the patient; a second sensor comprising a motion sensor configured to be attached to the patient's torso and measure a motion signal from the patient; a processing system configured to be worn on the patient's body and to be operably connected to the first sensor to receive a first signal representing at least one of the impedance pneumography, ECG, and PPG signals, and to be connected to the second sensor to receive a second signal representing the motion signal, the processing system configured to: A) i) process the motion signal to determine an initial respiratory rate; ii) process the first signal with a digital filter determined from the initial respiratory rate to determine a third signal; and iii) process the third signal to determine a value for the patient's respiration rate; or B) i) process the first signal to determine an initial respiratory rate; ii) process the motion signal with a digital filter determined from the initial respiratory rate to determine a third signal; and iii) process the third signal to determine a final value for the patient's respiration rate. a first sensor selected from the group consisting of: i) an impedance pneumography sensor comprising at least two electrodes and an impedance pneumography processing circuit configured to process signals from the two electrodes to measure an impedance pneumography signal from the patient; ii) an ECG sensor comprising at least two electrodes and an ECG processing circuit configured to process signals from the two electrodes to measure an ECG signal from the patient; and iii) a PPG sensor comprising a light source, photodetector, and PPG processing circuit configured to process signals from the photodetector to measure a PPG signal from the patient; i) an impedance pneumography sensor comprising at least two electrodes and an impedance pneumography processing circuit configured to process signals from the two electrodes to measure an impedance pneumography signal from the patient; ii) an ECG sensor comprising at least two electrodes and an ECG processing circuit configured to process signals from the two electrodes to measure an ECG signal from the patient; and iii) a PPG sensor comprising a light source, photodetector, and PPG processing circuit configured to process signals from the photodetector to measure a PPG signal from the patient; a second sensor comprising a motion sensor configured to be attached to the patient's torso and measure a motion signal from the patient; a processing system configured to be worn on the patient's body and to be operably connected to the first sensor to receive a first signal representing at least one of the impedance pneumography, ECG, and PPG signals, and to be connected to the second sensor to receive a second signal representing the motion signal, the processing system configured to: A) i) process the motion signal to determine an initial respiratory rate; ii) process the first signal with a digital filter determined from the initial respiratory rate to determine a third signal; and iii) process the third signal to determine a value for the patient's respiration rate; or B) i) process the first signal to determine an initial respiratory rate; ii) process the motion signal with a digital filter determined from the initial respiratory rate to determine a third signal; and iii) process the third signal to determine a final value for the patient's respiration rate. A) i) process the motion signal to determine an initial respiratory rate; ii) process the first signal with a digital filter determined from the initial respiratory rate to determine a third signal; and iii) process the third signal to determine a value for the patient's respiration rate; or B) i) process the first signal to determine an initial respiratory rate; ii) process the motion signal with a digital filter determined from the initial respiratory rate to determine a third signal; and iii) process the third signal to determine a final value for the patient's respiration rate.