ABSTRACT

In recent years, Compressive Sensing (CS) theory has attracted wide attention from scholars. Its advantages are low computational complexity, excellent compression performance and the independence of the acquisition and reconstruction, making it particularly suitable for large-scale monitoring of distributed sensor networks. For compressive sampling characteristics, CS related research is tried to apply to impact monitoring,

3 RANDOM DEMODULATION THEORY

Suppose a continuous time signal x(t), which is sparse, and can be written as the linear combination of a series of basis functions

( )t ( )t= =

∑α Ψ 1

(1)

The above equation is the compressive sampling’s sparse model, and its vector and matrix representative for the discrete signal are, x = Ψα where

α = … = …

=

[ , , , ] [ ( ) ( ), , ( )]

( ) ( ) ...