摘要:
A method and system are presented for reconstructing an input field where the latter is sensed by a measurement system. The method comprises: providing measured data corresponding to output field of said measurement system; providing data about sparsity of the input field, and data about effective response function of the measurement system; and processing the measured data based on said known data, the processing comprising: determining a sparse vector as a function of said measured data, said data about the sparsity of the input field, and said data about the effective response function; and using the sparse vector for reconstructing the input information. The invention allows for sub-wavelength resolution in imaging applications, and allows for detection of very short pulses by slow detectors in some other applications.
摘要:
A method of reproducing an original analog signal modified by a distortion and sampled. The distortion may be linear or nonlinear, and the samples may be either ideal or non-ideal. The method determines a stationary point of a cost function based on an error vector. The method iteratively computes approximated analog signals until the approximated analog signals converge to the original analog signal. The method may utilize Fr?chet derivatives and Moore-Penrose pseudo inverse transformations in order to iteratively compute the original analog signal. An apparatus performing said method is also disclosed.
摘要:
A method for signal processing includes accepting an analog signal, which consists of a sequence of pulses (36A-36F) confined to a finite time interval. The analog signal is sampled at a sampling rate that is lower than a Nyquist rate of the analog signal and with samples taken at sample times that are independent of respective pulse shapes of the pulses and respective time positions of the pulses in the time interval. The sampled analog signal is processed.
摘要:
A method for signal processing includes distributing an analog input signal to a plurality of processing channels. In each processing channel, the input signal is mixed with a respective periodic waveform including multiple spectral lines, so as to produce a respective baseband signal in which multiple spectral slices of the input signal are superimposed on one another. The baseband signal produced in each of the processing channels is digitized, to produce a set of digital sample sequences that represent the input signal.
摘要:
A method of reproducing an original analog signal modified by a distortion and sampled. The distortion may be linear or nonlinear, and the samples may be either ideal or non-ideal. The method determines a stationary point of a cost function based on an error vector. The method iteratively computes approximated analog signals until the approximated analog signals converge to the original analog signal. The method may utilize Fr?chet derivatives and Moore-Penrose pseudo inverse transformations in order to iteratively compute the original analog signal. An apparatus performing said method is also disclosed.
摘要:
A timing skew estimation system is disclosed that includes a plurality of interleaved analog-to-digital converter circuits (ADCs), a timing mismatch estimation unit, and a correction unit. The timing mismatch estimation unit calculates a correlation between each of the plurality of ADCs. Then the timing mismatch estimation unit calculates a cost function for each of the plurality of ADCs, except the reference ADC. The timing mismatch estimation unit further calculates a gradient for each of the plurality of ADCs, except the reference ADC. The timing mismatch estimation unit also continually calculates the timing skew of each of the plurality of ADCs, except the reference ADC, as the sum of an immediately previous estimate of the timing skew of each ADC, except the reference ADC, and a product of a function of the gradient of each of the plurality of ADCs, except the reference ADC, and a step size, The correction unit continually corrects the output of each of the plurality of ADCs, except the reference ADC, based on the estimates of the timing skew of each of the plurality of ADCs, except the reference ADC. Eventually, the timing skew estimation system determines a converged estimate of the timing skew of each of the plurality of ADCs, except the reference ADC. A method of estimating timing skew and timing skew estimation circuitry are also disclosed.
摘要:
A timing skew estimation system is disclosed that includes a plurality of interleaved analog-to-digital converter circuits (ADCs), a timing mismatch estimation unit, and a correction unit. The timing mismatch estimation unit calculates a correlation between each of the plurality of ADCs. Then the timing mismatch estimation unit calculates a cost function for each of the plurality of ADCs, except the reference ADC. The timing mismatch estimation unit further calculates a gradient for each of the plurality of ADCs, except the reference ADC. The timing mismatch estimation unit also continually calculates the timing skew of each of the plurality of ADCs, except the reference ADC, as the sum of an immediately previous estimate of the timing skew of each ADC, except the reference ADC, and a product of a function of the gradient of each of the plurality of ADCs, except the reference ADC, and a step size, The correction unit continually corrects the output of each of the plurality of ADCs, except the reference ADC, based on the estimates of the timing skew of each of the plurality of ADCs, except the reference ADC. Eventually, the timing skew estimation system determines a converged estimate of the timing skew of each of the plurality of ADCs, except the reference ADC. A method of estimating timing skew and timing skew estimation circuitry are also disclosed.
摘要:
A method includes accepting an analog input signal that includes a sequence of pulses. The analog input signal is filtered so as to produce a filter output, using a filter whose time-domain response is confined to a finite time period and whose frequency-domain response is non-zero at a finite set of integer multiples of a frequency shift Δω, and is zero at all other integer multiples of Δω. The filter output is sampled so as to produce digital samples. Respective amplitudes and time positions of the pulses in the sequence are calculated based on the digital samples.
摘要:
A method for signal processing includes accepting an analog signal, which consists of a sequence of pulses confined to a finite time interval. The analog signal is sampled at a sampling rate that is lower than a Nyquist rate of the analog signal and with samples taken at sample times that are independent of respective pulse shapes of the pulses and respective time positions of the pulses in the time interval. The sampled analog signal is processed.
摘要:
A method includes accepting an analog input signal including a sequence of pulses of a given pulse shape. The analog input signal is distributed to multiple processing channels (40) operating in parallel. The analog input signal is sampled by performing, in each of the multiple processing channels, the operations of: mixing the analog input signal with a different, respective modulating waveform to produce a mixed signal; filtering the mixed signal; and digitizing the filtered mixed signal to produce a respective digital channel output.