Periodic signal processing method, periodic signal conversion method, periodic signal processing device, and periodic signal analysis method

1. A periodic signal processing method comprising:

extracting, from a signal having periodicity, a fundamental period of the signal in a temporal direction;

arranging n sets of time windows such that centers of each of the n sets of time windows are separated by a fraction 1/n of the fundamental period, where n is an integer equal to or larger than 2, so as to extract n sets of portions of different ranges from the signal having periodicity;

calculating n set of power spectrums for the n set of portions extracted by the respective time windows;

adding the whole n sets of power spectrums with a same ratio to obtain a first power spectrum,

calculating a second power spectrum by convolving a rectangular smoothing function having a width corresponding to a fundamental frequency in a frequency direction on the obtained first power spectrum,

wherein the extracting fundamental period, the arranging time windows, the calculating power spectrums, and the adding at least two of the calculated power spectrums are performed by a processor programmed to perform the extracting fundamental period, the arranging time windows, the calculating power spectrums, and the adding at least two of the calculated power spectrums.

2. A periodic signal analysis method, comprising:

performing the periodic signal processing method of claim 1 ;

dividing the first power spectrum by the second power spectrum;

obtaining a deviation spectrum with only a component due to periodicity obtained by subtracting 1 from a result obtained by the division of the first power spectrum; and

obtaining a value of the fundamental period by calculating a weighted Fourier transform.

3. A periodic signal analysis method, comprising:

performing the periodic signal processing method of claim 1 ; and

contracting or dilating a time axis with a ratio in inverse proportion to an instantaneous frequency of a frequency of a fundamental period; and, for a first signal having periodicity converted so as to apparently become a signal having a frequency of a predetermined fundamental period, calculating a ratio of a periodic component in the first signal as an absolute value of a signal, which is obtained by convolving a quadrature signal designed using a frequency of a fundamental period set in advance on a deviation spectrum with only a component due to periodicity obtained by subtracting 1 from a result obtained by dividing the first power spectrum by the second power spectrum, so as to calculate a ratio of an aperiodic component in the signal.

4. A periodic signal conversion method, comprising:

performing the periodic signal processing method of claim 1 ; and

converting the signal having periodicity into a different signal by using at least one of the calculated power spectrums and the first power spectrum.

5. A periodic signal conversion method, comprising:

performing the periodic signal processing method of claim 1 ; and

converting the signal having periodicity into a different signal by using the second power spectrum.

6. A periodic signal processing method, comprising:

extracting, from a signal having periodicity, a fundamental period of the signal in a temporal direction;

arranging n sets of time windows such that centers of each of the n sets of time windows are separated by a fraction 1/n of the fundamental time period, where n is an integer equal to or larger than 2, so as to extract n sets of portions of different ranges from the signal having periodicity;

calculating n sets of power spectrums for the n sets of portions extracted by the respective time windows;

adding the whole n sets of power spectrums with a same ratio to obtain a first power spectrum;

calculating a cumulative sum of the first power spectrum for every predetermined range in the frequency direction; and

calculating a difference in the cumulative sum of the first power spectra in the predetermined range between two points at a predetermined interval in the frequency direction and performing linear interpolation to obtain a smoothed power spectrum,

wherein the extracting fundamental period, the arranging time windows, the calculating power spectrums, and the adding groups of at least two of the calculated power spectrums are performed by a processor programmed to perform the extracting fundamental period, the arranging time windows, the calculating power spectrums, and the adding groups of at least two of the calculated power spectrums.

7. The periodic signal processing method of claim 6 , further comprising:

obtaining a second power spectrum by subjecting the smoothed power spectrum obtained by the linear interpolation to logarithmic transformation, predetermined correction, and exponential transformation.

8. A periodic signal analysis method, comprising:

performing the periodic signal processing method of claim 7 ;

dividing the first power spectrum by the second power spectrum;

obtaining a deviation spectrum with only a component due to periodicity obtained by subtracting 1 from a result obtained by the division of the first power spectrum; and

obtaining a value of the fundamental period by calculating a weighted Fourier transform.

9. A periodic signal conversion method, comprising

performing the periodic signal processing method of claim 7 ; and

converting the signal having periodicity into a different signal by using the second power spectrum.

10. A periodic signal analysis method, comprising:

performing the periodic signal processing method of claim 6 ; and

dividing the first power spectrum by the smoothed power spectrum;

obtaining a deviation spectrum with only a component due to periodicity obtained by subtracting 1 from a result obtained by the division of the first power spectrum; and

obtaining a value of the fundamental period by calculating a weighted Fourier transform.

11. A periodic signal conversion method, comprising:

performing the periodic signal processing method of claim 6 ; and

converting the signal having periodicity into a different signal by using the smoothed power spectrum.

12. A periodic signal processing device, comprising:

a fundamental period calculation unit configured to extract, from a signal having periodicity, a fundamental period of the signal in a temporal direction;

an extraction unit configured to arrange n sets of time windows such that centers of each of the n sets of time windows are separated by a fraction 1/n of the fundamental period, where n is an integer equal to or larger than 2, so as to extract n sets of portions of different ranges from the signal having periodicity;

a calculation unit configured to calculate n sets of power spectrums for the n sets of portions extracted by the respective time windows;

an addition unit configured to obtain a first power spectrum by adding the whole n sets of power spectrums with a same ratio; and

a convolution unit configured to calculate a second power spectrum by convolving a rectangular smoothing function having a width corresponding to a fundamental frequency in a frequency direction on the first power spectrum.