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

• US 8,160,194 B2
• Filed: 08/17/2009
• Issued: 04/17/2012
• Est. Priority Date: 03/26/2001
• Status: Expired due to Term

• Current Assignee: Qualcomm, Inc.
• Original Assignee: Qualcomm, Inc.
• Inventors: Vetterli, Martin, Marziliano, Pina, Blu, Thierry
• Primary Examiner(s): Ahn, Sam K
• Application Number:
  US12/542,353
• Publication Number:
  US 20100042374A1
• Time in Patent Office: 974 Days
• Field of Search: 375/263, 375/355, 375/340, 327/9, 327/33, 327/45, 327/91, 329/361, 348/392.1, 348/405.1, 348/424.1, 702/189
• US Class Current: 375/355
• CPC Class Codes: H03M 1/1285 Synchronous circular sampling, i.e. using undersampling of periodic input signals
• CPC Class Codes: H03M 1/66 Digital/analogue converters H03M1/001 – H03M1/10 take precedence
• CPC Class Codes: H04B 1/707 using direct sequence modulation
• CPC Class Codes: H04B 2201/70707 Efficiency-related aspects

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 (y_s[n], y(nT)) a set of weights (c_n, c_nr, c_k) and shifts (t_n, t_k) 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 weights (c_k) and shifted by the shifts (t_k). The sampling rate is at least equal to the rate of innovation (ρ) of the first signal (x(t)).

Claims

1. Reconstruction method for reconstructing a first signal (x(t)) from a set of sampled values (y_s[n], y[nT]) generated by sampling a second signal (y(t)) at a sub-Nyquist rate and at uniform intervals, comprising:

retrieving, from a set of sampled values which were generated by sampling the second signal (y(t)) at the sub-Nyquist rate and at the uniform intervals, a set of shifts (LA) and weights (c_n, c_nr, c_k) with which said first signal (x(t)) can be reconstructed.

2. An apparatus for reconstructing a first signal (x(t)) from a set of sampled values (y_s[n], y[nT]) generated by sampling a second signal (y(t)) at a sub-Nyquist rate and at uniform intervals, comprising:

a memory configured to store a set of sampled values which were generated by sampling the second signal (y(t)) at the sub-Nyquist rate and at the uniform intervals; and

a processor configured to retrieve, from the set of sampled values, a set of shifts (t_n,t_k) and weights (c_n, c_nr, c_k) with which said first signal (x(t)) can be reconstructed.

3. A non-transitory computer readable medium for reconstructing a first signal (x(t)) from a set of sampled values (y_s[n], y[nT]) generated by sampling the second signal (y(t)) at the sub-Nyquist rate and at the uniform intervals, having stored thereon instructions that when executed by a processor cause the processor to:

retrieve, from the set of sampled values which were generated by sampling the second signal (y(t)) at the sub-Nyquist rate and at the uniform intervals, a set of shifts (t_n,t_k) and weights (c_n, c_nr, c_k) with which said first signal (x(t)) can be reconstructed.

4. An apparatus for reconstructing a first signal (x(t)) from a set of sampled values (y_s[n], y[nT]) generated by sampling a second signal (y(t)) at a sub-Nyquist rate and at uniform intervals, comprising:

means for storing a set of sampled values which were generated by sampling the second signal (y(t)) at the sub-Nyquist rate and at the uniform intervals; and

means for retrieving, from the set of sampled values, a set of shifts and weights (c_n, c_nr, c_k) with which said first signal (x(t)) can be reconstructed.