Signal Reconstruction Based on Shannon Wavelet Transformation from Nonuniform Sampling

The spectral noise caused by nonuniformly sampling makes the bandwidth of non-band-limited signal wider, even becomes the nonuniformly sampled signal. The traditional Shannon sampling theory isn´t practical any more. This paper investigates the Shannon scaling function and wavelet function of the amplitude frequency characteristics, based on the orthogonal decomposition and reconstruction, which describes a new approach that can reconstruct the low frequency and high frequency parts of the original signal efficiently by the nonuniformly sampled signal and the convolution of the Shannon scaling function with wavelet function. The validity of this method has been verified by simulation experiments, which shows the method of Shannon wavelet transformation can reconstruct the non-band-limited signal when sampled nonuniformly.