一种基于小波的导数采样算法

研究了小波空间中的一种导数采样理论，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，可以利用对信号及其导数采样所得的样本求出其小波系数的估计值，进而得到信号的重建表达式。在信号重建的过程中用到的全是有限冲击响应滤波器，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0．11％。

Derivative Sampling Algorithm Based on Wavelet

A derivative sampling theory in wavelet space is studied, the precondition and theory basis beyond the Nyquist rate is given, and the sampling theory is extended to the non-bandlimited signal field. For any signal in the space spanned by compactly supported scaling function, its wavelet coefficients could be estimated by the samples of signal and its derivative, so the reconstruction expression is obtained. During the procedure of signal reconstruction, only finite impulse response （FIR） filters are used, thus reducing the difficulty of physical realization： The simulation result indicates that this method is effective, and the relative reconstruction error is less than 0.11%.