给定重构滤波器条件下连续信号的最佳离散表示

Optimal Discrete Representation of Continuous-Time Signals for Given Reconstruction Filter

在重构滤波器给定的条件下,导出了最小平方意义下连续信号的最佳离散表示的傅里叶变换。为了更适应于某些应用,在推导时采用了有别于通常的内积定义,该内积诱导出的范数考虑了信号的变化速率。最佳离散表示可通过对连续信号依次进行模拟滤波、等间隔采样和数字滤波获得。此外,还把结果推广到二维信号的情形。

For a given reconstruction filter, the Fourier transform of the optimal discrete representation of a continuous signal is derived in the least -squares sense. To be more suitable for some applications, the inner product used is different from ususal definition, the norm derived from which contains the contribution from the derivative of the signal. The optimal discrete representation can be obtained from the continuous signal by employing analog filtering, uniform sampling, and digital filtering successively. In addition, the two - dimensional case is considered.