Signal processors and methods for estimating transformations between signals with phase estimation
A phase estimation method estimates the phase of signal components using a point spread function. The method obtains a point spread function that expresses complex frequencies at a non integer location in terms of integral frequencies, for a complex frequency of a signal at a non integer location in a complex frequency domain. It obtains complex frequencies of the signal for the integral frequencies, and computes a sum of products of the complex frequencies of the signal at the integral frequencies with the corresponding complex values of the point spread function to provide an estimate of phase of the signal at the non integer location.
1. In a detector of an embedded signal in an image, a method of computing an estimate of phase of the embedded signal in the image, the method comprising:
for a complex frequency of the embedded signal at a non integer location in a complex frequency domain, obtaining a point spread function that expresses complex frequencies at the non integer location in terms of frequencies at integer locations;
obtaining complex frequencies of the image for the frequencies at integer locations;
computing a sum of products of the complex frequencies of the image at the frequencies at integer locations with the corresponding complex values of the point spread function to provide an estimate of phase of the embedded signal at the non integer location; and
determining a difference between the estimate of the phase and an expected phase of the embedded signal to detect the embedded signal in the image.
2. The method of claim 1 wherein the image signal comprises an image signal sampled from an image sensor.
3. The method of claim 1 wherein the embedded signal comprises a set of signal components, and the non integer location comprises a location of one of the signal components.
4. The method of claim 3 wherein the signal components include a peak and the location of one of the signal components is a location of the peak.
5. The method of claim 1 wherein the embedded signal includes one or more peaks, and the point spread function is used to determine phase of one or more of the peaks at a non-integer location in the complex frequency domain.
6. The method of claim 5 wherein the point spread function is used to determine a geometric transformation of the embedded signal.
7. The method of claim 5 wherein the embedded signal comprises at least a portion of a digital watermark signal embedded in another signal.
8. A non-transitory computer readable medium, on which is stored instructions of a detector of an embedded signal in an image, the instructions, which, when executed by one or more processors, perform a method of computing an estimate of phase of the embedded signal in the image, the method comprising:
for a complex frequency of the embedded signal at a non integer location in a complex frequency domain, obtaining a point spread function that expresses complex frequencies at the non integer location in terms of frequencies at integer locations;
obtaining complex frequencies of the image for the frequencies at integer locations;
computing a sum of products of the complex frequencies of the image at the frequencies at integer locations with the corresponding complex values of the point spread function to provide an estimate of phase of the embedded signal at the non integer location; and
determining a difference between the estimate of the phase and an expected phase of the embedded signal to detect the embedded signal in the image.
9. A circuit in a detector of an embedded signal in an image, the circuit comprising:
means for obtaining a point spread function that expresses complex frequencies at a non integer location in terms of frequencies at integer locations for a complex frequency of the embedded signal at the non integer location in a complex frequency domain;
means for obtaining complex frequencies of the image for the frequencies at integer locations; and
means for computing a sum of products of the complex frequencies of the signal at the frequencies at integer locations with the corresponding complex values of the point spread function to provide an estimate of phase of the embedded signal at the non integer location.
10. The circuit of claim 9 including an image sensor for obtaining the image signal.
11. The circuit of claim 9 wherein the embedded signal comprises a set of signal components, and the non integer location comprises a location of one of the signal components.
12. The circuit of claim 11 wherein the signal components include a peak and the location of one of the signal components is a location of the peak.
13. The circuit of claim 9 wherein the embedded signal includes one or more peaks, and the point spread function is used to determine phase of one or more of the peaks at a non-integer location in the complex frequency domain.
14. The circuit of claim 13 wherein the point spread function is used to determine a geometric transformation of the embedded signal.
15. The circuit of claim 13 wherein the embedded signal comprises at least a portion of a digital watermark signal embedded in another signal.
16. The circuit of claim 9 comprising a point spread function table and product and sum operators to apply the point spread function.