System and method for analysis and reconstruction of variable pulse-width signals having low sampling rates

• US 9,275,013 B2
• Filed: 03/13/2013
• Issued: 03/01/2016
• Est. Priority Date: 03/16/2012
• Status: Expired due to Fees

• Current Assignee: Qualcomm, Inc.
• Original Assignee: Qualcomm, Inc.
• Inventors: Baechler, Gilles, Hormati, Ali
• Primary Examiner(s): DIETRICH, JOSEPH M
• Application Number:
  US13/800,754
• Publication Number:
  US 20130245471A1
• Time in Patent Office: 1,084 Days
• Field of Search: 600/509
• US Class Current: 1/1
• CPC Class Codes: A61B 5/0006 ECG or EEG signals
• CPC Class Codes: A61B 5/347 Detecting the frequency distribution of signals
• CPC Class Codes: A61B 5/7257 using Fourier transforms
• CPC Class Codes: G06F 17/141 Discrete Fourier transforms

Abstract

Systems and methods are described herein for applying a predefined functional shape to coefficients of a discrete Fourier transform of a waveform. The waveform may based, at least in part, on an electro-cardiogram (ECG). The predefined functional shape may be parabolic, and may be defined on a logarithmic scale. The application of a predefined functional shape may allow a more accurate reconstruction of a waveform to be generated at a lower sampling rate.

Claims

1. A computer implemented method of reconstructing a time domain waveform from a compressed original time domain waveform comprising:

receiving, in a processor, parameters defining a compressed form of the original time domain waveform;

generating, with the processor, discrete Fourier transform (DFT) coefficients from the parameters;

adjusting without zeroing, with the processor, the amplitudes of at least some of the generated DFT coefficients to more closely fit the amplitudes of the at least some of the generated DFT coefficients to a predefined functional shape; and

performing, with the processor, an inverse discrete Fourier transform (IDFT) on a set of DFT coefficients including the adjusted DFT coefficients to produce a reconstructed time domain waveform,

wherein the original time domain waveform is an electro-cardiogram (ECG) signal collected from ECG electrodes and the predefined functional shape is determined based at least in part on the ECG signal.

2. The method of claim 1, wherein the predefined functional shape is parabolic on a logarithmic scale.

3. The method of claim 1, further comprising deriving the parameters and storing the parameters for reconstruction.

4. The method of claim 1, wherein the parameters are derived from time domain samples of the original time domain waveform.

5. The method of claim 4, wherein the time domain samples are spaced at less than 120 Hz.

6. The method of claim 4, wherein the parameters represent characteristics of each of a series of pulses that model the original time domain waveform, and wherein the characteristics include at least a peak position, a peak amplitude, and a pulse width.

7. The method of claim 4, wherein the parameters are derived by a method comprising:

obtaining, by at least one processor, a series of at least MM discrete Fourier transform coefficients of an N sample time domain ECG signal, where MM is greater than 2K;

determining, by the at least one processor, K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving, by the at least one processor, a location and width of K pulses; and

deriving, by the at least one processor, one or both of a symmetric and asymmetric amplitude for each of the K pulses.

8. The method of claim 2, wherein the parameters are derived by a method comprising:

obtaining, by at least one processor, a series of at least MM discrete Fourier transform coefficients of an N sample time domain signal, where MM is greater than 2K;

determining, by the at least one processor, K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving, by the at least one processor, a location and width of K pulses; and

deriving, by the at least one processor, one or both of a symmetric and asymmetric amplitude for each of the K pulses.

9. The method of claim 1, wherein the adjusting comprises transforming a first set of generated DFT coefficients according to the formula:

adjusted

10. The method of claim 9, wherein α

and β

are derived by minimizing the formula;

∥

log X[m]−

α

m²−

β

∥

² over {α

,β

}

using a second set of generated DFT coefficients different from the first set.

11. The method of claim 2, wherein the adjusting comprises transforming a first set of generated DFT coefficients according to the formula:

adjusted

12. The method of claim 11, wherein α

and β

are derived by minimizing the formula;

∥

log X[m]−

α

m²−

β

∥

² over {α

,β

}

using a second set of generated DFT coefficients different from the first set.

13. The method of claim 12, wherein the parameters are derived by a method comprising:

obtaining, by at least one processor, a series of at least MM discrete Fourier transform coefficients of an N sample time domain ECG signal, where MM is greater than 2K;

determining, by the at least one processor, K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving, by the at least one processor, a location and width of K pulses; and

deriving, by the at least one processor, one or both of a symmetric and asymmetric amplitude for each of the K pulses.

14. A processing apparatus comprising:

a memory having stored therein parameters defining a compressed form of an original time domain waveform;

a processor configured to;

retrieve the parameters;

generate discrete Fourier transform (DFT) coefficients from the parameters;

adjust without zeroing the amplitudes of at least some of the generated DFT coefficients to more closely fit the amplitudes of the at least some of the generated DFT coefficients to a predefined functional shape; and

perform an inverse discrete Fourier transform (IDFT) on a set of DFT coefficients including the adjusted DFT coefficients to produce a reconstructed time domain waveform,

wherein the original time domain waveform is an electro-cardiogram (ECG) signal collected from ECG electrodes and the predefined functional shape is determined based at least in part on the ECG signal.

15. The apparatus of claim 14, wherein the predefined functional shape is parabolic on a logarithmic scale.

16. The apparatus of claim 14, wherein the processor is configured to derive the parameters and store the parameters in the memory.

17. The apparatus of claim 16, wherein the parameters are derived from time domain samples of the original time domain waveform.

18. The apparatus of claim 17, wherein the time domain samples are spaced at less than 120 Hz.

19. The apparatus of claim 17, wherein the parameters represent characteristics of each of a series of pulses that model the original time domain waveform, and wherein the characteristics include at least a peak position, a peak amplitude, and a pulse width.

20. The apparatus of claim 17, wherein the processor is configured to derive the parameters by a method comprising:

obtaining a series of at least MM discrete Fourier transform coefficients of an N sample time domain ECG signal, where MM is greater than 2K;

determining K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving a location and width of K pulses; and

deriving one or both of a symmetric and asymmetric amplitude for each of the K pulses.

21. The apparatus of claim 15, wherein the processor is configured to derive the parameters by a method comprising:

obtaining a series of at least MM discrete Fourier transform coefficients of an N sample time domain signal, where MM is greater than 2K;

determining K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving a location and width of K pulses; and

deriving, by the at least one processor, one or both of a symmetric and asymmetric amplitude for each of the K pulses.

22. The apparatus of claim 14, wherein the adjusting comprises transforming a first set of generated DFT coefficients according to the formula:

adjusted

23. The apparatus of claim 22, wherein α

and β

are derived by minimizing the formula;

∥

log X[m]−

α

m²−

β

∥

² over {α

,β

}

using a second set of generated DFT coefficients different from the first set.

24. The apparatus of claim 15, wherein the adjusting comprises transforming a first set of generated DFT coefficients according to the formula:

adjusted

25. The apparatus of claim 24, wherein α

and β

are derived by minimizing the formula;

∥

log X[m]−

α

m²−

β

∥

² over {α

,β

}

using a second set of generated DFT coefficients different from the first set.

26. The apparatus of claim 25, wherein the processor is configured to derive the parameters by a method comprising:

obtaining a series of at least MM discrete Fourier transform coefficients of an N sample time domain ECG signal, where MM is greater than 2K;

determining K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving a location and width of K pulses; and

deriving one or both of a symmetric and asymmetric amplitude for each of the K pulses.

27. The apparatus of claim 14, further comprising an antenna coupled to the processor, and wherein the processor is configured to receive the parameters wirelessly with the antenna and store the parameters in the memory.

28. The apparatus of claim 27, additionally comprising a body mountable device, the body mountable device comprising:

ECG electrodes;

an analog to digital converter;

a second antenna; and

a second processor, wherein the second processor is configured to receive time domain samples of signals generated by the ECG electrodes, derive the parameters from the time domain samples, and transmit the parameters with the second antenna.

29. The apparatus of claim 28, wherein the second processor is configured to derive the parameters by a method comprising:

obtaining a series of at least MM discrete Fourier transform coefficients of an N sample time domain signal, where MM is greater than 2K;

determining K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving a location and width of K pulses; and

deriving one or both of a symmetric and asymmetric amplitude for each of the K pulses.

30. A non-transitory, computer readable medium comprising instructions that when executed cause a processor to perform a method comprising:

receiving, in the processor, parameters defining a compressed form of an original time domain waveform;

generating, with the processor, discrete Fourier transform (DFT) coefficients from the parameters;

adjusting without zeroing, with the processor, the amplitudes of at least some of the generated DFT coefficients to more closely fit the amplitudes of the at least some of the generated DFT coefficients to a predefined functional shape;

performing, with the processor, an inverse discrete Fourier transform (IDFT) on a set of DFT coefficients including the adjusted DFT coefficients to produce a reconstructed time domain waveform,

wherein the original time domain waveform is an electro-cardiogram (ECG) signal collected from ECG electrodes and the predefined functional shape is determined based at least in part on the ECG signal.

31. The medium of claim 30, wherein the method further comprises deriving the parameters and storing the parameters for reconstruction.

32. The medium of claim 31, wherein deriving the parameters comprises:

obtaining a series of at least MM discrete Fourier transform coefficients of an N sample time domain ECG signal, where MM is greater than 2K;

determining K roots of an annihilator polynomial using the MM discrete Fourier transform coefficients;

based at least in part on the determined roots, deriving a location and width of K pulses; and

deriving one or both of a symmetric and asymmetric amplitude for each of the K pulses.

33. The medium of claim 30, wherein the adjusting comprises transforming a first set of generated DFT coefficients according to the formula:

adjusted

34. The medium of claim 33, wherein α

and β

are derived by minimizing the formula;

∥

log X[m]−

α

m²−

β

∥

² over {α

,β

}

using a second set of generated DFT coefficients different from the first set.