Sampling method, reconstruction method, and device for sampling and/or reconstructing signals
AssigneeQUALCOMM Incorporated
InventorsMartin Vetterli, Pina Marziliano, Thierry Blu
Life of this patent
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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 (γ(t)) weighted by the weigths (ck) and shifted by the shifts (tk). The sampling rate is at least equal to the rate of innovation (ρ) of the first signal (x(t)).
Claims22
A method implemented in an apparatus for reconstructing a first signal (x(t)), the method comprising:
- sampling a second signal (y(t)) at a sub-Nyquist rate and at uniform intervals;
- generating a set of sampled values (ys[n], y(nT)) from the second signal (y(t));
- retrieving from said set of sampled values a set of shifts (tn, tk) and weights (cn, cnr, ck);
- and
- reconstructing the first signal (x(t)) based on the set of shifts (tn, tk) and weights (cn, cnr, ck).
A method implemented in an apparatus for sampling a first signal (x(t)), wherein said first signal (x(t)) can be represented over a finite time interval (τ) by the superposition of a finite number (K) of known functions (δ(t), γ(t), γr(t)) delayed by arbitrary shifts (tn, tk) and weighted by arbitrary amplitude coefficients (cn, ck), said method comprising:
- convoluting said first signal (x(t)) with a sampling kernel ((φ(t), φ(t)) and using a regular sampling frequency (f, 1/T),
- choosing said sampling kernel ((φ(t), φ(t)) and said sampling frequency (f, 1/T) such that sampled values (ys[n], y(nT)) completely specify said first signal (x(t)), and
- reconstructing said first signal (x(t)),
- wherein said sampling frequency (f, 1/T) is lower than the frequency given by the Shannon theorem, but greater than or equal to twice said finite number (K) divided by said finite time interval (τ).
Dependencies are inferred from the claim text.