Compressed sensing signal collection method based on filtering

Abstract

A compressed sensing signal collection method based on filtering includes the following steps: firstly, sensing equipment is used for collecting target signals x (t) in an independent sampling period and carries out digital quantification on the signals in an analog / digit (A / D) mode. Secondly, the dimension of the quantified signals x (i) is reduced. Lastly, the signals with the reduced dimension are reconfigured. The t means the sampling time, and the i means the sequence of the quantified signals. The detailed method of dimension-reduction of the quantified signals is that the quantified signals respond to a difference equation of a filter through finite impulse, and the difference equation is that i= 1, ..., M, wherein h (0), ..., h (L-1) is the coefficients of the filter. The design constructs a following toeplitz measurement array based on a compressed sensing signal collection framework of the filter, and the toeplitz measurement array is that i= 1, ..., M is observed, wherein b1,..., bL are treated as coefficients of the filter. The singular value of a sub-array phi FT is an arithmetic value of a characteristic value of a Gramm array which is that G (phi F, T) = phi ` FT phi FT, all the characteristic values that lambada i belongs to (1- delta K, 1+ delta K), wherein i= 1, ..., T of G (phi F, T) are tested, and the original signals are reconfigured by solving the following l1 optimization problems.

Description

technical field [0001] The technical solution belongs to the technical field of signal processing, and specifically relates to a filter-based compression sensing signal acquisition method. Background technique [0002] With the development of digital signal processing, the ability of the system to acquire data is continuously improved, and the amount of data to be processed is also increasing. There are two key difficulties in the field of traditional signal processing based on Shannon sampling theorem: (1) The Nyquist sampling frequency is too high for broadband signals, resulting in too much sampled data; (2) Many systems use sampling first and then compression The data acquisition mode wastes not only sensor elements, but also time, storage space and bandwidth resources. These limit the traditional signal processing methods to some extent. In recent years, D.Donoho, E.Candès and T.Tao et al. proposed a new sampling technology - Compressed Sensing (Compressed Sensing, CS...

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Problems solved by technology

Literature [9] constructs a polynomial measurement matrix, whose size is not arbitrary, which limits the compression rate and affects the applicability; Literature [10] proposes a structured random matrix, but there is a gap in the reconstruction effect between it and the Gaussian random measurement matrix; Literature [11] constructed a circulatory matrix through a row of elements, and applied it to sparse channel estimation, but the number of observations required for accurate reconstruction was not significantly reduced; Literature [12] used an analog filter for downsampling, and designed a pseudo Toeplitz measurement matrix, but no significant improvement in signal reconstruction compared to random matrices

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