Sampling method, reconstruction method, and device for sampling and/or reconstructing signals
First Claim
1. Reconstruction method for reconstructing a first signal (x(t)) from a set of sampled values (ys[n], y(nT)) generated by sampling a second signal (y(t)) at a sub-Nyquist rate and at uniform intervals, comprising the step of retrieving from said set of sampled values a set of shifts (tn, tk) and weights (cn, cnr, ck) with which said first signal (x(t)) can be reconstructed.
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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)).
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Citations
24 Claims
- 1. Reconstruction method for reconstructing a first signal (x(t)) from a set of sampled values (ys[n], y(nT)) generated by sampling a second signal (y(t)) at a sub-Nyquist rate and at uniform intervals, comprising the step of retrieving from said set of sampled values a set of shifts (tn, tk) and weights (cn, cnr, ck) with which said first signal (x(t)) can be reconstructed.
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23. Sampling method 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), γ
r(t)) delayed by arbitrary shifts (tn, tk) and weighted by arbitrary amplitude coefficients (cn, ck),said method comprising the convolution of said first signal (x(t)) with a sampling kernel ((φ
(t), φ
(t)) and using a regular sampling frequency (f, 1/T),said sampling kernel ((φ
(t), φ
(t)) and said sampling frequency (f, 1/T) being chosen such that the sampled values (ys[n], y(nT)) completely specify said first signal (x(t)), allowing a perfect reconstruction of said first signal (x(t)),characterized in that 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
). - View Dependent Claims (24)
- ) by the superposition of a finite number (K) of known functions (δ
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