Research On Finite-Rate-of-Innovation Sampling Method Of Asymmetric Pulse Streams

Traditional sampling scheme must obey the Nyquist sampling theorem,which states that the original bandlimited analog signal can be recovered from its digital samples without distortion when the sampling rate is no lower than twice the maximum frequency of the original analog signal.However,with the fast development of information and communication technology,the signal bandwidth becomer higher and higher,which gradually leads to explosion of some problems under the direction of this traditional signal processing method and brings increasing pressure on signal acquisition and processing devices.In recent years,a new sampling method — Finite Rate of Innovation(FRI),has been developed to effectively reduce the pressure on system sampling,processing,storing and transmission.In the FRI theory special sampling schemes are designed according to the parametric characteristics of FRI signals,which achieves a much lower sampling rate nearly equal to the innovation rate as well as precise signal reconstruction from low-rate samples.One of the typical FRI signals is pulse streams.However,the pulse streams in practical applications are often asymmetric due to distortion.Considering that symmetric pulse streams are often studied in classical FRI theory,a problem of model mismatch exists.In this paper,focusing on the FRI sampling method of asymmetric pulse streams,the main studies are as follows:(1)Study the FRI sampling theory and the existing FRI sampling methods of asymmetric pulse streams.Firstly study the FRI signal model,the basic FRI sampling scheme and the FRI recovery algorithms.Then introduce the existing FRI models of asymmetric pulse streams and corresponding FRI sampling methods.Finally analyze the property of each model through MATLAB simulation experiments,which provides theoretical basis for the following method improvement of asymmetric pulse streams by the FRI theory.(2)Propose an improved FRI sampling method of asymmetric pulse streams.Firstly propose a model of differentiated VPW pulse streams based on the existing VPW-FRI(Variable Pulse Width with Finite Rate of Innovation)model and study its FRI sampling method.Then focus on the application of differentiated VPW pulse streams in FRI sampling of non-ideal piecewise polynomials.Finally study the FRI sampling process of differentiated VPW pulse streams and its application in nonideal piecewise polynomial FRI sampling through MATLAB simulations,including principle verification,model anti-noise ability analysis and model matching performance comparison when matching real signals.Experiment results prove that the improved models we have proposed are able to precisely recover the parameters by sub-Nyquist sampling and certain recovery algorithms.They also gain better model matching performance compared with the original FRI models.(3)Design the experimental platform for FRI sampling of asymmetric pulse streams.In the hardware system the So S sampling kernel is designed as a sixth-order Chebyshev I-type low-pass filter,and NI PXIe devices are applied to construct the PXI system,which achieves several functions such as analog signal output and data acquisition.The software system is programmed by Lab VIEW in order to control the PXI system,calibrate the weighted coefficients of the So S(Sum of Sincs)sampling kernel,store the sampled data and reconstruct the test signal.(4)Verify the FRI sampling process of asymmetric pulse streams by hardware experiments.Hardware experiments are performed on the platform in order to verify the FRI sampling process of asymmetric pulse streams and the application of the improved model in non-ideal piecewise polynomial FRI sampling process.The results show that our proposed model of differentiated VPW pulse streams achieves sub-Nyquist sampling as well as accurate reconstruction for asymmetric pulse streams with arbitrary pulse shape.Moreover,when applying the model of differentiated VPW pulse streams in FRI sampling of non-ideal piecewise polynomials,the locations of discontinuity points and the uncertain transition zones of the non-ideal piecewise polynomials can be precisely recovered.Therefore,the model of differentiated VPW pulse streams has a wider applicability in comparison with the other FRI models of asymmetric pulse streams.