Frequency profiles for non-contact range measurement with multi-scale analysis

1. A method for constructing a frequency profile of an emitted signal suitable for use in a non-contact ranging system with multi-scale spectral analysis, comprising:

determining N stepped frequency chirps, wherein each frequency chirp of the N stepped frequency chirps has a linear FM modulation of a predetermined bandwidth and slope, and wherein a starting frequency for each of the plurality of stepped frequency chirps is chosen so that a non-linear step profile is created which extends over a predetermined total bandwidth,

sorting the plurality of N stepped frequency chirps into P sub-sequences, where P is equal to the product of decimation factors to be used in the multi-scale spectral analysis, and

ordering the P sub-sequences end to end in time;

wherein each of the plurality of N stepped frequency chirps is represented only once in the P sub-sequences and each of the P sub sequences extends to at least 90% of the predetermined total bandwidth.

2. The method of claim 1 wherein the duration of emitting the P sub-sequences or a multiple of the P sub-sequences is equal to the duration of a longest duration frame in the multi-scale spectral analysis or a multiple thereof.

3. The method of claim 1 wherein, on each analysis scale, the frame length is an integer multiple of the sub-sequence length.

4. The method of claim 2 further comprising:

prior to sorting the plurality of N stepped frequency chirps into P sub sequences, enumerating groups of the N stepped frequency chirps as G 0 through G (N−1) to define even-indexed groups of frequency chirps and odd-indexed groups of frequency chirps; and

reordering one of the even-indexed groups of frequency chirps and the odd-indexed groups of frequency chirps in time to begin at an end of the other one of the even-indexed groups of frequency chirps and the odd-indexed groups of frequency chirps and in reverse order.

5. The method of claim 4 wherein sorting the N stepped frequency chirps into P sub-sequences comprises:

re-enumerating the reordered frequency chirps as C 0 through C (N−1) ; and

sorting the reordered frequency chirps into P sub-sequences, wherein {sub-sequence} n ={C n , C (n+P) , C (n+2P) , C (n+3P) , . . . } n , where n=0 to (P−1).

6. The method of claim 1 wherein the slope of each of the plurality of frequency chirps is selected to resolve a minimum range target frequency from a zero range frequency.

7. The method of claim 1 wherein the fastest sampling rate is equal to or a multiple of the step rate for the plurality of N stepped frequency chirps.

8. The method of claim 1 wherein a total bandwidth of the non-linear step profile is chosen to attain a desired distance resolution in frequency modulated continuous wave radar.

9. The method of claim 8 wherein the predetermined total bandwidth of the non-linear step profile is greater than or equal to 1.5 GHz.

10. The method of claim 1 wherein the non-linear step profile is chosen to control the magnitude of unwanted spectral side lobes.

11. The method of claim 10 wherein the non-linear step profile comprises a parametric frequency profile or a tapering distribution.