Automatic wavelet generation system and method

• US 6,539,319 B1
• Filed: 10/30/1998
• Issued: 03/25/2003
• Est. Priority Date: 10/30/1998
• Status: Expired due to Fees

• Current Assignee: Caterpillar Incorporated
• Original Assignee: Caterpillar Incorporated
• Inventors: Grichnik, Anthony J.
• Primary Examiner(s): WACHSMAN, HAL D
• Application Number:
  US09/183,187
• Time in Patent Office: 1,607 Days
• Field of Search: 702/75, 702/17, 702/66, 702/74, 702/76, 702/77, 702/72, 702/73, 702/71, 702/112, 702/124, 702/126, 702/183, 702/189-191, 702/197, 702/198, 702/193-195, 702/FOR.134, 702/FOR.135, 702/FOR.164, 702/FOR.166, 702/FOR.168, 702/FOR.170, 702/FOR.171, 702/FOR.103, 702/FOR.104, 702/FOR.107, 702/FOR.108, 702/FOR.110, 324/76.19, 324/76.21, 324/76.22, 324/76.28, 324/76.29, 324/76.31, 324/76-7-, 324/76.68, 342/192, 342/196, 342/90, 382/280, 382/235, 382/243, 382/274, 382/248, 382/250, 382/253, 382/239, 382/232, 382/233, 708/203, 708/403-405, 708/300, 708/309, 708/311, 708/819, 708/821, 708/400, 704/205, 704/206, 704/201, 704/227, 704/226, 704/229, 704/230, 348/398.1, 348/403.1, 348/408.1, 375/240.11
• US Class Current: 702/75
• CPC Class Codes: G06F 17/17 Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method G06F17/18 takes precedence ; interpolation for numerical control G05B19/18

Abstract

A wavelet generator for defining wavelets that represent a first signal includes a programmable filter bank, a frequency band controller coupled to the programmable filter bank, and a wavelet constructor coupled to the programmable filter bank. The programmable filter bank is operable to receive the first signal, and filter the first signal based upon a plurality of frequency bands to obtain a plurality of frequency band signals that each represent a frequency band of the first signal. The frequency band controller is also operable to receive the first signal. Moreover, the frequency band controller is further operable to obtain the plurality of frequency bands from the first signal, and program the programmable filter bank with the plurality of frequency bands. The wavelet constructor is operable to receive the plurality of frequency band signals.

Claims

1. A method for defining a plurality of wavelets that represent a first signal, comprising the steps of:

generating a first frequency band signal representative of a first frequency band of said first signal;

generating a second frequency band signal representative of a second frequency band of said first signal;

defining a first wavelet of said plurality of wavelets to represent said first frequency band signal; and

defining a second wavelet of said plurality of wavelets to represent said second frequency band signal.

2. The method of claim 1, further comprising the step of:

analyzing said first signal to obtain a plurality of characteristic frequency boundaries for said first signal,

wherein said step of generating said first frequency band signal comprises the step of defining said first frequency band based upon said plurality of characteristic frequency boundaries.

3. The method of claim 2, wherein said step of generating said first frequency band signal further comprises the steps of:

defining a first pass band based upon said plurality of characteristic frequency boundaries; and

filtering said first signal with respect to said first pass band in order to obtain said first frequency band signal representative of said first frequency band of said first signal.

4. The method of claim 1, further comprising the steps of:

analyzing said first signal to obtain a plurality of characteristic frequency boundaries for said first signal; and

decimating said plurality of characteristic frequency boundaries in order to define a plurality of frequency bands,

wherein said step of generating said first frequency band signal comprises the step of selecting said first frequency band from said plurality of frequency bands.

5. The method of claim 4, wherein said decimating step comprises the steps of:

selecting every N^th characteristic frequency boundary of said plurality of characteristic frequency boundaries, where N is an integer; and

defining said plurality of frequency bands based upon said selected characteristic frequency boundaries.

6. The method of claim 4, wherein said analyzing step comprises the steps of:

calculating an accumulative spectral power plot of said first signal, and

selecting said plurality of characteristic frequency boundaries based upon said accumulative spectral power plot.

7. The method of claim 1, wherein said first wavelet defining step comprises the step of:

utilizing autoregression to generate a plurality of values representative of said first frequency band signal.

8. A wavelet generator for defining a plurality of wavelets that represent a first signal, comprising a processor, and a memory having stored therein a plurality of instructions which when executed by said processor cause said processor to:

generate a first frequency band signal representative of a first frequency band of said first signal;

generate a second frequency band signal representative of a second frequency band of said first signal;

define a first wavelet of said plurality of wavelets to represent said first frequency band signal; and

define a second wavelet of said plurality of wavelets to represent said second frequency band signal.

9. The wavelet generator of claim 8, wherein said plurality of instructions when executed by said processor further cause said processor to:

analyze said first signal to obtain a plurality of characteristic frequency boundaries for said first signal; and

define said first frequency band based upon said plurality of characteristic frequency boundaries.

10. The wavelet generator of claim 9, wherein said plurality of instructions when executed by said processor further cause said processor to:

define a first pass band based upon said plurality of characteristic frequency boundaries; and

filter said first signal with respect to said first pass band in order to obtain said first frequency band signal.

11. The wavelet generator of claim 8, wherein said plurality of instructions when executed by said processor further cause said processor to:

analyze said first signal to obtain a plurality of characteristic frequency boundaries for said first signal;

decimate said plurality of characteristic frequency boundaries in order to define a plurality of frequency bands; and

select said first frequency band from said plurality of frequency bands.

12. The wavelet generator of claim 8, wherein said plurality of instructions when executed by said processor further cause said processor to:

analyze said first signal to obtain a plurality of characteristic frequency boundaries for said first signal;

decimate said plurality of characteristic frequency boundaries by selecting every N^th characteristic frequency boundary of said plurality of characteristic frequency boundaries, where N is an integer;

define a plurality of frequency bands based upon said selected characteristic frequency boundaries; and

select said first frequency band from said plurality of frequency bands.

13. The wavelet generator of claim 8, wherein said plurality of instructions when executed by said processor further cause said processor to:

calculate an accumulative spectral power plot from said first signal;

select a plurality of characteristic frequency boundaries for said first signal based upon said accumulative spectral power plot;

decimate said plurality of characteristic frequency boundaries in order to define a plurality of frequency bands; and

select said first frequency band from said plurality of frequency bands.

14. The wavelet generator of claim 8, wherein said plurality of instructions when executed by said processor further cause said processor to:

generate said first wavelet by utilizing autoregression to generate a plurality of values representative of said first frequency band signal.

15. A wavelet generator for defining a plurality of wavelets that represent a first signal, comprising:

a programmable filter bank operable to (i) receive said first signal, and (ii) filter said first signal based upon a plurality of frequency bands to obtain a plurality of frequency band signals that each represent a frequency band of said first signal; and

a frequency band controller coupled to said programmable filter bank, said frequency band controller operable to (i) receive said first signal, (ii) obtain said plurality of frequency bands from said first signal, and (iii) program said programmable filter bank with said plurality of frequency bands; and

a wavelet constructor coupled to said programmable filter bank, said wavelet constructor operable to (i) receive said plurality of frequency band signals, and (ii) generate a separate wavelet for each of said plurality of frequency band signals.

16. The wavelet generator of claim 15, wherein said wavelet constructor comprises:

an autoregression component that is operable to (i) receive a first frequency band signal of said plurality of frequency band signals, and (ii) generate a first wavelet comprising a plurality of values representative of said first frequency band signal.

17. The wavelet generator of claim 15, wherein said programmable filter bank comprises:

a first programmable filter module that is operable to filter said first signal to produce a first frequency band signal which differs in phase from a first frequency band of said first signal by a first phase difference amount; and

a second programmable filter module that is operable to filter said first signal to produce a second frequency band signal which differs in phase from a second frequency band of said first signal by a second phase difference amount,

wherein said first phase difference amount and said second phase difference amount are substantially equal.

18. The wavelet generator of claim 17, wherein:

said first phase difference amount and said second phase difference amount are substantially equal to zero.

19. The wavelet generator of claim 18, further including:

a spectral analyzer operable to (i) receive said first signal, and (ii) generate a frequency spectrum from said first signal;

a boundary extractor coupled to said spectral analyzer, said boundary extractor operable to (i) receive said frequency spectrum from said spectral analyzer, and (ii) obtain from said frequency spectrum a plurality of characteristic frequency boundaries for said first signal;

wherein said frequency band controller comprises a decimator coupled to said boundary extractor, said decimator operable to (i) receive said plurality of characteristic frequency boundaries from said boundary extractor, and (ii) decimate said plurality of characteristic frequency boundaries in order to obtain said plurality of frequency bands.

20. The wavelet generator of claim 19, wherein said boundary extractor comprises:

an integrator coupled to said spectral analyzer, said integrator operable to (i) receive said frequency spectrum, and (ii) generate an accumulative sum signal that is representative of the accumulative spectral power of said frequency spectrum; and

a linear regression component coupled to said integrator, said linear regression component operable to (i) receive said accumulative sum signal, (ii) fit a first line to said accumulative sum signal, said first line representing the slope of a portion of said accumulative sum signal, and (iii) cause a first frequency to be included in said plurality of characteristic boundary frequencies in response to a first accumulative spectral power value of said accumulative sum signal deviating from the magnitude of said first line at said first frequency by more than a threshold amount.