Methods, Devices and Systems for Receiving and Decoding a Signal in the Presence of Noise Using Slices and Warping

1. A method, comprising: receiving a signal, by an analog front-end of a receiver, the signal encoding a data packet; sampling, by and analog-to-digital converter, the received signal; generating, by a controller, and storing, by the controller in a memory coupled to the controller, a plurality of slices comprising pairs of values for each of a selected number of samples of the signal; detecting, by the controller, a presence of and decoding, by the controller, the data packet from the stored slices; forming, by the controller, a filter having a predetermined pass-band by combining, by the controller, a number of the plurality of slices; and re-tuning, by the controller, a center frequency of the filter from a first center frequency to a second center frequency that is different from the first center frequency using the stored slices by warping the stored slices from which the filter was formed by rotating the respective pairs of values by a quantity.

2. The method of claim 1 , wherein generating and storing, by the controller, are carried out as the received signal is sampled.

3. The method of claim 1 , further comprising discarding, by the controller, the sampled signal as the slice is generated and stored.

4. The method of claim 1 , wherein generating and storing, by the controller, are carried out with constituent values of each of the slices being generated using a first reference function and a second reference function that is in quadrature with the first reference function.

5. The method of claim 1 , wherein generating, by the controller, each of the plurality of slices comprises: Correlating, by the controller, samples of the signal with a first reference template; generating, by the controller, a first value of the pair of values; correlating, by the controller, the selected number of samples of the signal with a second reference template; and generating, by the controller, a second value of the pair of values.

6. The method of claim 5 , wherein the first reference template comprises a cosine function at a reference frequency and the second reference template comprises a sine function at the reference frequency.

7. The method of claim 6 , wherein the first value of the pair of values of the slice comprises a dot product of the sampled signal and the cosine function at the reference frequency and the second value of the pair of values of the slice comprises a dot products of the sampled signal and the sine function at the reference frequency.

8. The method of claim 1 , wherein a bandwidth of the filter is related to the number of combined slices.

9. The method of claim 8 , wherein when a first number of slices are combined, the filter has a first bandwidth and wherein when a second number, greater than the first number, of slices are combined, the filter has a second bandwidth that is narrower than the first bandwidth.

10. The method of claim 1 , wherein detecting, by the controller, the presence of the data packet comprises detecting, by the controller, a carrier frequency within the predetermined pass-band of the filter formed by the plurality of slices.

11. The method of claim 1 , wherein detecting, by the controller, further comprises re-tuning, by the controller, the center frequency of the filter from a first center frequency to a second center frequency that is different from the first center frequency using the stored slices.

12. The method of claim 1 , wherein the quantity comprises a rotation angle, a scaling factor and indices associated with the slices from which the filter was formed.

13. The method of claim 1 , wherein the quantity comprises a sum of a phase angle from a reference frequency and a product of a rotation angle and a slice index.

14. A signal receiver, comprising: an analog front-end configured to receive a signal, the signal encoding a data packet; an analog-to-digital converter (ADC) configured to sample a received signal; a memory; a controller coupled to the memory and configured to: generate and store, in the memory, a slice comprising a pair of values for each of a selected number of samples of the signal; detect a presence of and decode the data packet from the stored slices; combine a number of the slices to form a filter having a predetermined pass-band; and re-tune a center frequency of the filter by warping the slices from which the filter was formed by rotating the respective pairs of values by a quantity.

15. The signal receiver of claim 14 , wherein the controller is configured to generate and store the slices as the ADC samples the received signal.

16. The signal receiver of claim 14 , wherein the controller is further configured to discard the sampled signal as the slices are generated and stored.

17. The signal receiver of claim 14 , wherein the controller is further configured to generate each of the slices such that constituent values thereof are generated using a first reference function and a second reference function that is in quadrature with the first reference function.

18. The signal receiver of claim 14 , wherein the memory is configured to store at least a first reference template and a second reference template and wherein the controller is further configured to correlate the selected number of cycles of the sampled signal with the first reference template to generate a first value of the pair of values and to correlate the selected number of samples of the signal with the second reference template to generate a second value of the pair of values.

19. The signal receiver of claim 18 , wherein the first reference template comprises a first reference function at a reference frequency and the second reference template comprises a second reference function at the reference frequency.

20. The signal receiver of claim 19 , wherein the first reference function is in quadrature with the second reference function.

21. The signal receiver of claim 20 , wherein the first reference function comprises a cosine function and the second reference function comprises a sine function.

22. The signal receiver of claim 21 , wherein the first value of the pair of values of the slice comprises a dot product of the sampled signal and the cosine function at the reference frequency and the second value of the pair of values of the slice comprises a dot product of the sampled signal and the sine function at the reference frequency.

23. The signal receiver of claim 14 , wherein a bandwidth of the filter is related to the number of combined slices.

24. The signal receiver of claim 23 , wherein when a first number of slices are combined, the filter has a first bandwidth and wherein when a second number, greater than the first number, of slices are combined, the filter has a second bandwidth that is narrower than the first bandwidth.

25. The signal receiver of claim 14 , wherein the controller is further configured to detect the presence of the data packet by detecting a carrier frequency within the pass-band of the filter formed by combining the slices.

26. The signal receiver of claim 14 , wherein the controller is further configured to re-tune, using the stored slices, a center frequency of the filter from a first center frequency to a second center frequency that is different from the first center frequency.

27. The signal receiver of claim 14 , wherein the quantity comprises a rotation angle, a scaling a factor and respective slice indices associated with the slices from which the filter was formed.

28. The signal receiver of claim 27 , wherein the scaling factor is an integer.

29. The signal receiver of claim 27 , wherein the scaling factor comprises an algebraic expression.