We give characterizations of stable scaling functions with compact band regions, which have the oversampling property.

Following our former works on regular sampling in wavelet subspaces, the paper provides two algorithms to estimate the truncation error and aliasing error respectively when the theorem is applied to calculate concrete signals. Furthermore the shift sampling case is also discussed. Finally some important examples are calculated to show the algorithm.

The fact that bounded interval band orthonormal scaling function shows oversampling property is demonstrated. The truncation error is estimated when scaling function with oversampling property is used to recover signals from their discrete samples.

The paper obtains an algorithm to estimate the irregular sampling in wavelet subspaces. Compared to our former work on the problem, the new estimate is relaxed for some wavelet subspaces.

An oversampling theorem for regular sampling in wavelet subspaces is established. The sufficient-necessary condition for which it holds is found. Meanwhile the truncation error and aliasing error are estimated respectively when the theorem is applied to reconstruct discretely sampled signals. Finally an algorithm is formulated and an example is calculated to show the algorithm.

The paper provides the algorithm to estimate the deviation bound admitting to recovering irregularly sampled signals in wavelet subspaces, which does not need the symmetricity sampling constraint of Paley-Wiener's and relaxes the deviation bounds in some wavelet subspaces. Meanwhile the method does not need the continuity and decay constraints imposed on scaling functions by Liu-Walter and Chen-Itoh-Shiki.

A new method to obtain the coefficients of Daubechies's scaling functions is given, in which it is not necessary to find the complex zeros of polynomials. Consequently it becomes easier to obtain the coefficients of arbitrary order from 2 to 40 with high accuracy.

In this paper, new wavelet bases are presented. We address problems associated with the proposed matched filter in multirate systems, using an optimum receiver that maximises the SNR at the sampling instant. To satisfy the Nyquist (ISI-free transmission) and matched filter (maximum SNR at the sampling instant) criteria, the overall system filtering strategy requires to split the narrowest filter equally between transmitter and receiver. In data transmission systems a raised-cosine filter is therefore often used to bandlimit signals from which wavelet bases are derived. Sampling in multiresolution subspaces is also discussed.

This paper is concened with the design and implementation of a 2-channel, 2-dimensional filter bank using rectangular (analog/digital) and quincunx (digital/digital) sampling. The associated analog low-pass filters are separable where as the digital low-pass filters are non-separable for a minimum sampling density requirement. The digital low-pass filters are Butterworth type filters, N = 9, realized as LWDFs. They, when itterated, approximate a valid scaling function (raised-consine scaling function). The obtained system can be used to compute a discrete wavelet transform.