Signal processing method and apparatus
A method and apparatus for estimating the frequency of a dominant periodic component in an input signal by modelling the input signal using auto-regressive models of several different orders to generate candidate frequencies for the periodic component, generating synthetic sinusoidal signals of each of the candidate frequencies, and calculating the cross-correlation of the synthetic signals with the original signal. The frequency of whichever of the synthetic signals has the highest cross-correlation with the original signal is taken as the estimate of the frequency for the dominant periodic component of the input signal. The method may be applied to any noisy signal which has a suspected periodic component, for example physiological signals such as photoplethysmogram signals, and in the estimation of heart rate and breathing rate from such physiological signals.
1. A method of analyzing an input signal to estimate the frequency of a periodic signal therein comprising:
receiving the input signal;
generating frequency domain candidates for the periodic signal by performing spectral analysis on the input signal to detect spectral components of the input signal, the detected spectral components constituting the frequency domain candidates;
for each frequency domain candidate generating a synthetic signal of the same frequency;
calculating in time domain a measure of the similarity of each synthetic signal with the input signal;
defining a similarity threshold;
outputting as the estimate of the frequency of the periodic signal the frequency of the synthetic signal with maximum similarity with the input signal; and
inhibiting the outputting if the similarity of the synthetic signal with the maximum similarity with the input signal is below the similarity threshold.
2. A method according to claim 1 wherein the measure of similarity is correlation or cross-correlation.
3. A method according to claim 1 wherein the spectral analysis is by autoregressive modelling.
4. A method according to claim 3 wherein a plurality of autoregressive models of different orders are fitted to the input signal.
5. A method according to claim 4 wherein the plurality of autoregressive models comprise models of order 2 to 20.
6. A method according to claim 3 wherein synthetic signals are generated for each pole in the fitted autoregressive models.
7. A method according to claim 3 wherein synthetic signals are generated for only poles in the fitted autoregressive models which correspond to a predetermined allowed frequency range for the periodic signal.
8. A method according to claim 3 wherein synthetic signals are generated for only poles in the fitted autoregressive models which have a predetermined magnitude.
9. A method according to claim 3 wherein synthetic signals are generated for only the dominant poles in the fitted autoregressive models.
10. A method according to claim 1 wherein the frequency domain candidates are generated by selecting a plurality of different frequencies within a predetermined frequency range.
11. A method according to claim 10 wherein the plurality of different frequencies are evenly spaced from each other over the frequency range.
12. A method according to claim 1 wherein the input signal is temporally windowed, for example from 5 to 60 seconds long, and the steps of calculating the similarity and outputting a frequency estimate are performed for each window.
13. A method according to claim 12 wherein the windows are overlapping windows, for example with an overlap from 0.5 to 10 seconds.
14. A method according to claim 1 , wherein the input signal is obtained by de-trending and filtering a noisy signal.
15. A method according to claim 14 wherein the input signal is obtained by resampling the de-trended and filtered noisy signal.
16. A method according to claim 1 , wherein the synthetic signal is sinusoidal.
17. A method according to claim 1 , wherein the input signal is a time series of image intensity data.
18. A method according to claim 1 wherein the input signal is video image data comprising a time series of intensity data for each color channel.
19. A method according to claim 1 wherein the input signal is a measurement of a physiological parameter of a human or animal subject.
20. A method according to claim 19 wherein the periodic signal is the heart rate or respiration rate of the subject.
21. A computer program comprising program code means for executing on a computer system the method of claim 1 .
22. Apparatus for analyzing an input signal to estimate the frequency of a periodic signal therein comprising:
an input for receiving the input signal;
a processor for processing input signal;
the processor being configured to execute the steps of claim 1 ; the apparatus further comprising an output to output as the frequency estimate the frequency of the synthetic signal with the maximum cross-correlation with the input signal.