Period estimation of an almost periodic signal using persistent homology with application to respiratory rate measurement
Date
2017Source Title
IEEE Signal Processing Letters
Print ISSN
1070-9908
Publisher
Institute of Electrical and Electronics Engineers Inc.
Volume
24
Issue
7
Pages
958 - 962
Language
English
Type
ArticleItem Usage Stats
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Abstract
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.
Keywords
PeriodicityPersistent homology
Pyro-electric infrared (PIR) sensor
Respiratory rate (RR)
Topological data analysis