Patent Document ID: 8787501
Application ID: 12686183
Patent Flag: 1

Claim One:
1. A method of reconstructing a pair of signals, comprising: observing with a first sensor first samples of a first signal; observing with a second sensor second samples of a second signal, wherein the first signal is linked to the second signal by an unknown filter; exploiting the knowledge that the first and the second signal are linked by the unknown filter for reconstructing said first signal and said second signal from said first samples and said second samples, wherein each of a number of the first samples and a number of the second samples observed is below a minimal number of samples given by a Nyquist relation; receiving discrete Fourier transform (DFT) coefficients of said first signal and said second signal, the DFT coefficients including K+1 coefficients for each of the first signal and the second signal and complementary subsets of remaining DFT coefficients for each of the first signal and the second signal, wherein K is a number of non-zero elements of an impulse response of the unknown filter; computing 2K consecutive DFT coefficients of the unknown filter and building a matrix using the received DFT coefficients of the first and second signals and an annihilating filter technique, wherein said matrix is a Toeplitz matrix and has rank-K; obtaining the impulse response of the unknown filter using the computed 2K DFT coefficients; reconstructing the first signal using the impulse response of the unknown filter and the received DFT coefficients of the second signal; and reconstructing the second signal using the impulse response of the unknown filter and the received DFT coefficients of the first signal.