Method and circuit for real time frequency analysis of a non-stationary signal

• US 7,076,380 B2
• Filed: 07/02/2002
• Issued: 07/11/2006
• Est. Priority Date: 07/04/2001
• Status: Expired due to Fees

• Current Assignee: Airbus Operations SAS (Airbus SE)
• Original Assignee: Airbus France
• Inventors: Michel, Patrice
• Primary Examiner(s): NGHIEM, MICHAEL P
• Application Number:
  US10/482,499
• Publication Number:
  US 20040189277A1
• Time in Patent Office: 1,470 Days
• Field of Search: 702/17, 702/66, 702/70, 702/71, 702 75- 77, 702/79, 702/190, 702/194, 702/196, 702/197, 704/205, 708/311, 708/312, 708/314, 708/403, 708/404, 708/405, 324/76.39, 324/76.41, 324/76.42, 324/76.44, 324/76.45
• US Class Current: 702/75
• CPC Class Codes: G06F 17/14 Fourier, Walsh or analogous domain transformations , e.g. Laplace, Hilbert, Karhunen-Loeve, transforms for correlation function computation G06F17/156; spectrum analysers G01R23/16

Abstract

Method for analysing the frequency in real-time of a non-stationary signal and corresponding analysis circuit.

According to the invention, the signal is sampled, it is digitised, it is broken up into sub-bands. In each sub-band, the signal is modelled by an auto-regressive filter the transfer function of which is of the form 1/A(z). By an adaptive method that is recursive in time and in order, all the polynomials A(z) that have a degree between 1 and a maximum value are calculated. The order of the model is estimated and the polynomial that has this order is retained. The roots of this polynomial are calculated and the components are monitored. The frequency and the amplitude of the sinusoidal components of the signal are thus obtained.

Application in aeronautics, electromagnetic, mechanics, seismic prospecting, zoology, etc.

Claims

1. Method for analysing the frequency in real-time of a non-stationary signal, characterised in that said method includes the following operations:

A) the signal is sampled at a frequency (fe) at least equal to twice the highest expected frequency and the samples obtained are digitised,

B) the sampled and digitised signal is broken up into sub-bands by applying the samples to a bank of digital filters with adjacent pass bands,

C) the signal is modelled in each sub-band by an auto-regressive filter, the transfer function of which is 1/A(z), where A(z) is a polynomial of the complex variable z=exp(j2π

f/fe) by implementing an adaptive method that is recursive in time and in order, all the polynomials A(z) with a degree between 1 and a maximum value selected in advance are calculated,

D) the order of the model is estimated and of all the calculated polynomials the one retained is the one having said order,

E) using a recursive algorithm, at least some complex roots of the polynomial selected are calculated,

F) from the phase of the roots obtained, the corresponding frequencies are determined, and from the frequencies, the square of the distance separating a current point corresponding to a component at one sampling instant from the points obtained at the previous sampling instant, the previous point which minimises said square is made to correspond to the current point and the different points are connected by minimising a weighted function of said square and the amplitudes are sought for the sinusoidal components that have said frequencies and which minimise the quadratic error between the sum of said components and the signal for analysis, the sinusoidal components are monitored by calculating, in a frequency-amplitude plane.

2. Method according to claim 1, wherein, after the sampled and digitised signal is broken up into sub-bands, each sub-band is spread in frequency by decimation of the samples.

3. Method according to claim 1, wherein the signal is broken up into sub-bands by a bank of compact support (finite impulse response) orthogonal filters.

4. Method according to claim 1, wherein a cascade of filtering stages is used each possessing 2^k filters where k is the rank of the stage.

5. Method according to claim 1, wherein the signal is broken up into sub-bands by non-compact support (infinite impulse response) filters.

6. Method according to claim 5, wherein the filters are orthogonal.

7. Method according to claim 5, wherein non-orthogonal filters are used followed by Hilbert filters.

8. Method according to claim 1, wherein in the operation D, the model order is estimated from a criterion based on the maximum a posteriori (MAP) of the model existence probability.

9. Method according to claim 1, wherein, from knowledge of modules of the polynomial roots, the mode existence probability corresponding to said modules is evaluated relative to a probability distribution law selected in advance, and from the number of probable modes thus evaluated the order of the polynomial modelling the signal for analysis is deduced.

10. Method according to claim 9, wherein the distribution law is a two parameter gamma law.

11. Circuit for analysing the frequency in real-time of a non-stationary signal for implementing the method according to claim 1, characterised in that said circuit includes:

A) a circuit for sampling the signal at a frequency (fe) at least equal to twice the highest expected frequency and the samples obtained are digitised,

B) a circuit for breaking up the sampled and digitized signal into sub-bands including a bank of digital filters with adjacent pass bands,

C) for each sub-band, a signal modelling means including an auto-regressive filter, the transfer function of which is 1/A(z), where A(z) is a polynomial of the complex variable z=exp(j2π

f/fe), said signal modelling means implementing an adaptive method recursive in time and in order, and being able to calculate all the polynomials A(z) with a degree between 1 and a maximum value selected in advance,

D) a means for estimating the model order and for retaining among all the polynomials calculated the one which possesses said order,

E) a calculation circuit implementing a recursive algorithm, able to calculate at least some complex roots of the selected polynomial,

F) means for determining, from the phase of the roots obtained, the corresponding frequencies, and for monitoring the sinusoidal components, said determining means being able to calculate, in a frequency-amplitude plane, the square of the distance separating a current point corresponding to a component at one sampling instant from the points obtained at the previous sampling instant, to make the previous point which minimises said square correspond to the current point and to relate the different points by minimising a weighted function of said square, said determining means being able, from the frequencies, to seek the amplitudes of the sinusoidal components having said frequencies and which minimise the quadratic error between the sum of said components and the signal for analysis.