一种基于FIR滤波器的非均匀小波周期采样方法

针对Shannon采样定理只能处理带限信号和要求采样率不低于Nyquist率的缺陷,研究了小波空间中的一种非均匀周期采样理论,给出了定理成立的条件及其突破Nyquist率限制的理论依据,将采样理论扩展到了非带限信号领域。对于紧支尺度函数张成的子波空间中的任意信号,可以利用非均匀周期采样所得的样本以及正交镜像滤波器理论求出其小波系数的估计值,进而得到信号的重建表达式。该方法在信号重建的过程中用到的全是有限冲击响应滤波器,避免了无限冲击响应滤波器的出现,降低了实际物理实现的难度。计算机仿真结果表明该方法是切实有效的,信号重建的相对误差小于1%。

Nonuniform Periodic Sampling Theory in Wavelet Space Based on FIR Filter

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%.