Time-frequency techniques have difficulties in yielding efficient online algorithms for almost periodic signals. We describe a new topological method to find the period of signals that have an almost periodic waveform. Proposed method is applied to signals received from a pyro-electric infrared sensor array for the online estimation of the respiratory rate (RR) of a person. Timevarying analog signals captured from the sensors exhibit an almost periodic behavior due to repetitive nature of breathing activity. Sensor signals are transformed into two-dimensional point clouds with a technique that allows preserving the period information. Features, which represent the harmonic structures in the sensor signals, are detected by applying persistent homology and the RR is estimated based on the persistence barcode of the first Betti number. Experiments have been carried out to show that our method makes reliable estimates of the RR.