Apparatus and method for sampling and reconstruction of wide bandwidth signals below Nyquist rate
First Claim
1. A system of reconstructing data signals from one of incomplete, compressed or sparse measurements comprising:
- a receiver for receiving data signals from a target area,an analog to digital conversion system operatively connected to the receiver, the analog to digital conversion system digitizes a received data signal at a slower rate than a Nyquist minimum sampling rate to obtain a sub-Nyquist digitized output;
first and second dictionaries for storage of a plurality of time shifted data recovered from previously transmitted signals;
the first dictionary operating to store time shifted versions of previously transmitted signals which are sampled above the Nyquist minimum sample rate;
the second dictionary operating to store time shifted versions of previously transmitted signals which are sampled below the Nyquist minimum sample rate, andat least one processor for reconstruction of waveform signals;
the at least one processor operating to transform the sub-Nyquist digitized output from the analog to digital conversion system into an approximation of the received data signal using the first and second dictionaries to produce reconstruct the data signal.
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Abstract
A method and system of reconstructing data signals from one of incomplete measurements comprising a receiver for receiving data signals, an ADC system operatively connected to the receiver that digitizes the received data signal at a slower rate than the Nyquist rate to obtain sparse measurements; first and second dictionaries comprising a plurality of time shifted responses recovered from the data signal; the first dictionary comprising time shifted versions of the previously observed data signals which are sampled at or above the Nyquist minimum sample rate; the second dictionary comprising time shifted versions are sampled below the Nyquist minimum, and at least one processor for reconstruction of the waveform signals by transforming the sub-Nyquist digitized output using the first and second dictionaries to produce the data signal.
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Citations
20 Claims
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1. A system of reconstructing data signals from one of incomplete, compressed or sparse measurements comprising:
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a receiver for receiving data signals from a target area, an analog to digital conversion system operatively connected to the receiver, the analog to digital conversion system digitizes a received data signal at a slower rate than a Nyquist minimum sampling rate to obtain a sub-Nyquist digitized output; first and second dictionaries for storage of a plurality of time shifted data recovered from previously transmitted signals;
the first dictionary operating to store time shifted versions of previously transmitted signals which are sampled above the Nyquist minimum sample rate;
the second dictionary operating to store time shifted versions of previously transmitted signals which are sampled below the Nyquist minimum sample rate, andat least one processor for reconstruction of waveform signals;
the at least one processor operating to transform the sub-Nyquist digitized output from the analog to digital conversion system into an approximation of the received data signal using the first and second dictionaries to produce reconstruct the data signal. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20)
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15. A method for reconstructing data signals from one of incomplete, compressed or sparse measurements comprising:
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providing a receiver for receiving data signals from a target area, providing an analog to digital conversion system operatively connected to the receiver, the analog to digital conversion system digitizing a received data signal at a slower rate than a Nyquist minimum sampling rate to obtain a sub-Nyquist digitized output, creating first and second dictionaries for storage of a plurality of time shifted data recovered from previously transmitted signals;
the first dictionary operating to store time shifted versions of previously transmitted signals which are sampled above the Nyquist minimum sample rate;
the second dictionary operating to store time shifted versions of previously transmitted signals which are sampled below the Nyquist minimum sample rate,providing at least one processor for reconstruction of waveform signals;
the at least one processor operating to transform the sub-Nyquist digitized output from the analog to digital conversion system into an approximation of the received data signal using the first and second dictionaries to produce the data signal.
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Specification