US 11,907,326 B1 · Systems and method for determining frequency coefficients of signals

Abstract

A system for determining the frequency coefficients of a one or multi-dimensional signal that is sparse in the frequency domain includes determining the locations of the non-zero frequency coefficients, and then determining values of the coefficients using the determined locations. If N is total number of frequency coefficients across the one or more dimension of the signal, and if R is an upper bound of the number of non-zero ones of these frequency coefficients, the systems requires up to (O(Rlog(R) (N))) samples and has a computation complexity of up to O(Rlog2(R) log (N). The system and the processing technique are stable to low-level noise and can exhibit only a small probability of failure. The frequency coefficients can be real and positive or they can be complex numbers.

Claims14

Dependent claims

A method for identifying magnitudes of frequency components of a signal f(x) received by a receiver, the method comprising:

obtaining a first plurality of sets of signal samples received by an antenna or a sensor of the receiver, each set comprising a plurality of samples of the signal f(x), a cardinality of each set being greater than an upper bound (R) of a number of non-zero frequency components of the signal f(x) and less than a number of samples N of the signal f(x) according to a Nyquist rate,
wherein obtaining each set of signal samples comprises subsampling the signal f(x) by the receiver, at least one set of signal samples determines a support set S;
and
computing by a processor an initial set of frequency coefficients f0 using the support set S and the first plurality of sets of signal samples, the support set S identifying indices of the non-zero frequency components of the signal f(x).

1 more element

A system for identifying magnitudes of frequency components of a signal f(x) received by a receiver, the system comprising:

a first processor;
and
a first memory in electrical communication with the first processor, the first memory comprising instructions which, when executed by a processing unit comprising at least one of the first processor and a second processor, and in electronic communication with a memory module comprising at least one of the first memory and a second memory, program the processing unit to:
obtain a first plurality of sets of signal samples received by an antenna or a sensor of the receiver, each set comprising a plurality of samples of the signal f(x), cardinality of each set being greater than an upper bound (R) of a number of non-zero frequency components of the signal f(x) and less than a number of samples N of the signal f(x) according to a Nyquist rate,
wherein to obtain each set of signal samples the processing unit is configured to subsample the signal f(x) by the receiver, at least one set of signal samples determines a support set S;
and
compute an initial set of frequency coefficients f0using a support set S and the first plurality of sets of signal samples, the support set S identifying indices of the non-zero frequency components of the signal f(x).

4 more elements

Dependencies are inferred from the claim text.

Systems and method for determining frequency coefficients of signals

Life of this patent

Systems and method for determining frequency coefficients of signals

Life of this patent

Abstract

Claims14