Sampling method, reconstruction method, and device for sampling and/or reconstructing signals

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).