Analog Signal Processing Based On Compressive Sensing

Traditional analog signal processing conforms to Nyquist sampling theory, which will result in two problems:First, the data to be sampled is too massive, overburdening transmission channel and storage; Second, some analog signals with a wide bandwidth, need high sampling frequency beyond ADC's limits, such as RF signal.Despite wide spectrum range, some signals contain scarce information, making a great number of data sampled by front-end be disposed in rear-end processing. Therefore, this "processing after sampling" mode should be improved.In 2006, a new principle was proposed by Donoho:if the signal f can be represented by several coefficients or non-zero coefficients after orthogonal basisΨtransformation, original signal can be recovered by the product ofΨandΦwhich is noncoherent fromΨthis whole process is called compressive sensing theory. Compressive sensing theory is a novel signal processing concept, which abandons traditional "processing after sampling" mode, combines sampling with compressing, recovers original signal through a small quality of measurements, and reduces hardware load a lot.Based on predecessor's work, this thesis's contributions are listed as follows:1. This thesis studies sampling of continuous time signal, describes random modulation system which can realize precise recovery of original signal at a sampling rate lower than Nyquist sampling frequency. Sampling of analog signal can be achieved by mixing and filtering of analog signal and stretching spectrum to cover the entire frequency domain, which will reduce sampling rate. Then original signal is reconstructed by OMP in compressive sensing. Dynamic simulation of the whole system by Simulink has proven the correctness of the theoretical framework.2,This thesis discuses sampling of multiband bandlimitied signal, and introduces broadband signal modulation converter system, which can combine traditional signal processing with compressive sensing at sampling phase, and consists of two phases. At sampling phase, analog signal is input into multichannel simultaneously. It is multiplied with a band periodic signal, then the output is filtered by low pass filter, finally sampling is implemented at a low frequency rate. The output is non-zero band on the baseband. At reconstruction phase, frequency supports are solved, then OMP is ultilized to reconstruct. Thus, multiband analog signal can be processed at a low frequency. Simulation results demonstrate that reconstruction of multiband analog signal with noises can be realized by this system.