A family of nonorthogonal polynomial spline wavelet transforms is considered. These transforms are fully reversible and can be implemented efficiently. The corresponding wavelet functions have a compact support. It is proven that these B-spline wavelets converge to Gabor functions (modulated Gaussian) pointwise and in all L/sub p/-norms with 1>or=p+ infinity as the order of the spline (n) tends to infinity. In fact, the approximation error for the cubic B-spline wavelet (n=3) is already less then 3%; this function is also near-optimal in terms of its time/frequency localization in the sense that its variance product is within 2% of the limit specified by the uncertainty principle.
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机译：考虑了一系列非正交多项式样条小波变换。这些转换是完全可逆的，可以有效地实现。相应的小波函数具有紧凑的支持。证明这些B样条小波逐点收敛到Gabor函数（调制的高斯），并且在所有L / sub p /范数中，随着样条（n）的阶趋于无穷大，它们的无穷大为1>或= p +。实际上，三次B样条小波（n = 3）的近似误差已经小于3％。就其时间/频率定位而言，此函数在其方差积在不确定性原理指定的极限的2％以内的意义上也接近最佳。
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