Method, apparatus and system for digital data resampling utilizing fourier series based interpolation

• US 20040230391A1
• Filed: 05/15/2003
• Published: 11/18/2004
• Est. Priority Date: 05/15/2003
• Status: Active Grant

• Current Assignee: Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Original Assignee: Northrop Grumman Corporation
• Inventors: Jorgensen, Jerry D.
• Granted Patent: US 6,915,225 B2
• Time in Patent Office: Days
• US Class Current: 702/77
• CPC Class Codes: H03H 17/0621 with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing
• CPC Class Codes: H03H 2017/0214 with input-sampling frequency and output-delivery frequency which differ, e.g. interpolation, extrapolation; anti-aliasing

Abstract

The present invention provides a methodology, apparatus and system for resampling digital data utilizing a Fourier series based interpolation engine 104. A quick means to up-sample or down-sample data is provided without requiring computationally intensive processing. This is accomplished by utilizing low order coefficients of terms of a complete Fourier series expansion for a continuous signal. The summation of the expansion is limited to input samples immediately adjacent in time to the desired output. Generally speaking, the output is normally required to be a constant sampling rate, therefore, the input and output rates are related by an integer ratio. This ratio can be greater or smaller than one, providing up-sampling or down-sampling as appropriate. By employing the present invention, a DSP engine can be constructed that is adjustable to any ratio of sampling rates in a computationally efficient manner with low RMS error while preserving convolution through the resampling process.

Claims

1. A digital data resampling system, comprising:

a digital sampling engine that receives digital data, and determines a Fourier series summation range that is immediately adjacent in time to a desired digital data output, the engine resampling the digital data utilizing a Fourier series expansion summed over the Fourier series summation range.

2. The system of claim 1 employing the following equation:

3. The system of claim 1, further comprising an “

n”

-tap FIR (finite impulse response) filter.

4. The system of claim 1 employed in a conventional DSP system so as to provide additional functionality gains to the conventional DSP system.

5. A vehicle employing the system of claim 1.

6. A computing system employing the system of claim 1.

7. A method of resampling a digital signal, comprising:

receiving at least one input sample of a continuous signal sampled at a first sample rate;

formulating a Fourier series expansion of the continuous signal;

establishing a limited range of the Fourier series expansion, the limited range approximately including at least one input sample immediately adjacent in time to at least one desired output sample of a second sample rate; and

summing terms of the Fourier series expansion of the continuous signal over the limited range.

8. The method of claim 7, further including:

obtaining a continuous signal; and

sampling the continuous signal at the first sample rate to provide at least one input sample.

9. The method of claim 8, the first sample rate and the second sample rate are related by an integer ratio.

10. The method of claim 9, wherein the first sample rate is an input sample rate and the second sample rate is an output sample rate.

11. The method of claim 9 wherein the integer ratio is selected from a group consisting of smaller than one and greater than one.

12. The method of claim 7, further including:

formulating at least one coefficient derived from the Fourier series expansion and the limited range; and

multiplying at least one coefficient with at least one input sample to produce at least one output sample.

13. The method of claim 7, further including establishing a number of input samples based on a maximum desired throughput latency.

14. The method of claim 7, further including establishing a number of input samples based on a minimum desired continuous signal reproduction accuracy level.

15. A digital resampling device having a resampling rate related by an integer ratio to an input rate utilized in creating a set of input digital data, the digital sampling device resampling the input digital data at the resample rate while maintaining convolution of a continuous signal represented by the input digital data.

16. The digital sampling device of claim 15, the resampling rate having a range of 5 to 10 times the input rate for the input digital data.

17. The digital sampling device of claim 15, further including an RMS error less than applying linear interpolation to the input digital data to derive output digital data.

20. A system for converting signals from analog to digital, comprising:

an analog to digital converter; and

at least one digital resampling system as per claim 15.

21. The system of claim 20, further comprising at least two digital resampling systems as per claim 15 with at least one of the digital resampling systems having a different resampling rate.

22. The system of claim 21, at least one of the digital resampling systems having a resampling rate greater than 2, and typically in a range of 5 to 10 times, a highest frequency of interest.

23. The system of claim 20, further comprising at least two digital resampling devices as per claim 15 cascaded to allow an output of at least one digital resampling device to be an input of at least one digital resampling device.

24. The system of claim 23, further comprising at least one tap between digital resampling devices to allow for an output to a system.

25. The system of claim 20, further comprising at least two digital resampling devices as per claim 15 in parallel with an identical input to each digital resampling device.

29. A computer comprising the digital resampling system of claim 15.

30. A handheld electronic device comprising the digital resampling system of claim 15.

18. A digital data resampling system, comprising:

means to receive digital data and determine a Fourier series summation range that is immediately adjacent in time to a desired digital data output;

means to resample the digital data utilizing a Fourier series expansion summed over the Fourier series summation range; and

means to output the resampled digital data.

19. The system of claim 18, further including means to extend the Fourier series summation range based on a desired fidelity of the resampled digital data.

26. A method of resampling digital data, comprising:

determining a number of digital sample inputs;

determining a desired minimum fidelity for a desired digital output signal;

determining a desired maximum latency for processing a set of desired digital sample outputs;

determining a desired number of digital output samples;

calculating coefficients for processing the digital sample inputs based on a Fourier series expansion over a limited range, the limited range approximately including at least one input sample immediately adjacent in time to at least one desired output sample of a second sample rate;

inputting digital samples;

processing the digital samples by multiplying the digital samples by the coefficients; and

outputting a resampled set of digital samples.

27. The method of claim 26, further comprising:

determining if more digital samples are available for processing; and

determining if processing should continue when more digital samples are available.

28. The method of claim 26, further comprising:

determining if sampling parameters should be reconfigured; and

determining if the number of digital sample inputs should be changed based up a predetermined level of continuous signal reproduction accuracy.