Abstract: The present invention relates to a method of processing a signal which is received by a receiver, comprising, obtaining an analog signal (yt) based on another signal (xt) and noise; defining a sampling kernel based on the noise; and using the sampling kernel to obtain at least one sample (yn) from the analog signal (yt). The invention also relates to a corresponding apparatus; computer program product; headset; watch, and sensing device.

Abstract: A method of signal processing, comprising: obtaining a digital signal (yn) based on another signal (xt) and noise; and estimating information relating to the another signal (xt) by using a denoising process to produce a denoised signal (y?n) and by processing the denoised signal (y?n), wherein the denoised signal (y?n) produced by the denoising process has a substantially Finite Rate of Innovation.

Abstract: Reconstruction method for reconstructing a first signal (x(t)) regularly sampled at a sub-Nyquist rate, comprising the step of retrieving from the regularly spaced sampled values (ys[n], y(nT)) a set of weights (cn, cnr, ck) and shifts (tn, tk) with which said first signal (x(t)) can be reconstructed. The reconstructed signal (x(t)) can be represented as a sequence of known functions (?(t)) weighted by the weights (ck) and shifted by the shifts (tk). The sampling rate is at least equal to the rate of innovation (?) of the first signal (x(t)).

Abstract: Reconstruction method for reconstructing a first signal (x(t)) regularly sampled at a sub-Nyquist rate, comprising the step of retrieving from the regularly spaced sampled values (ys[n], y(nT)) a set of weights (cn, cnr, ck) and shifts (tn, tk) with which said first signal (x(t)) can be reconstructed. The reconstructed signal (x(t)) can be represented as a sequence of known functions (?(t)) weighted by the weights (ck) and shifted by the shifts (tk). The sampling rate is at least equal to the rate of innovation (?) of the first signal (x(t)).

Abstract: A reconstruction method for reconstructing a first signal from a set of sampled values generated by sampling a second signal at a sub-Nyquist rate and at uniform intervals, the method includes retrieving from the set of sampled values a set of shifts and weights with which the first signal can be reconstructed.

Abstract: Reconstruction method for reconstructing a first signal (x(t)) regularly sampled at a sub-Nyquist rate, comprising the step of retrieving from the regularly spaced sampled values (ys[n], y(nT)) a set of weights (cn, cnr, ck) and shifts (tn, tk) with which said first signal (x(t)) can be reconstructed. The reconstructed signal (x(t)) can be represented as a sequence of known functions (?(t)) weighted by the weigths (ck) and shifted by the shifts (tk). The sampling rate is at least equal to the rate of innovation (?) of the first signal (x(t)).

Abstract: Reconstruction method for reconstructing a first signal (x(t)) regularly sampled at a sub-Nyquist rate, comprising the step of retrieving from the regularly spaced sampled values (ys[n], y(nT)) a set of weights (cn, cnr, ck) and shifts (tn, tk) with which said first signal (x(t)) can be reconstructed. The reconstructed signal (x(t)) can be represented as a sequence of known functions (?(t)) weighted by the weights (ck) and shifted by the shifts (tk). The sampling rate is at least equal to the rate of innovation (?) of the first signal (x(t)).

Abstract: Signals, including signals from outside of the subspace of bandlimited signals associated with the Shannon theorem, are acquired while still providing an acceptable reconstruction. In some aspects a denoising process is used in conjunction with sparse sampling techniques. For example, a denoising process utilizing a Cadzow algorithm may be used to reduce the amount of noise associated with sampled information. In some aspects the denoising process may be iterative such that the denoising process is repeated until the samples are denoised to a sufficient degree. In some aspects, the denoising process converts a set of received samples into another set corresponding to a signal with a Finite Rate of Innovation (FRI), or to an approximation of such a signal. The disclosure relates in some aspects to combination of a denoising process with annihilating filter methods to retrieve information from a noisy, sparse sampled signal.

Abstract: Signals, including signals from outside of the subspace of bandlimited signals associated with the Shannon theorem, are acquired while still providing an acceptable reconstruction. In some aspects a denoising process is used in conjunction with sparse sampling techniques. For example, a denoising process utilizing a Cadzow algorithm may be used to reduce the amount of noise associated with sampled information. In some aspects the denoising process may be iterative such that the denoising process is repeated until the samples are denoised to a sufficient degree. In some aspects, the denoising process converts a set of received samples into another set corresponding to a signal with a Finite Rate of Innovation (FRI), or to an approximation of such a signal. The disclosure relates in some aspects to combination of a denoising process with annihilating filter methods to retrieve information from a noisy, sparse sampled signal.

Abstract: Reconstruction method for reconstructing a first signal (x(t)) regularly sampled at a sub-Nyquist rate, comprising the step of retrieving from the regularly spaced sampled values (ys[n], y(nT)) a set of weights (cn, cnr, ck) and shifts (tn, tk) with which said first signal (x(t)) can be reconstructed. The reconstructed signal (x(t)) can be represented as a sequence of known functions (?(t)) weighted by the weigths (ck) and shifted by the shifts (tk). The sampling rate is at least equal to the rate of innovation (?) of the first signal (x(t)).