Nonuniform Periodic Sampling Theory in Wavelet Space Based on FIR Filter
Liping Jiang · Modern Electronics Technique · 2008
Aiming at the drawback that Shannon theory can only process bandlimited signals and it requires the sampling rate is not less than Nyquist rate,this paper studies a nonuniform periodic sampling theory in wavelet space,then presents the precondition and theory base beyond the Nyquist rate.Sampling theory to the non-bandlimited signal field is enlarged.For any signal in the space spanned by compactly supported scaling function,its wavelet coefficients can be estimated by the nonuniform periodic samples and the quadrature mirror filter theory,then its reconstruction expression is gained.Only the finite impulse response filters but not the infinite impulse response filters are used in this method,which reduced the difficulty of physical realization.The simulation results indicate that the method is so effective that its relative reconstruction error is less then 1%.