Some new discrete biorthogonal wavelets constructed with Laguerre polynomials

Abstract

In this study, we present a new family of discrete wavelets which are constructed with the help of Laguerre polynomials and the Daubechies biorthogonal wavelets construction method. Our aim is to propose the discrete version of some previously constructed continuous Laguerre wavelets and also to present a method of discrete wavelets construction by several iterations. With this scheme, we use two different sets of finite impulse response filters for the signal decomposition and their duals for reconstruction. The quadruplet finite impulse response filters respect the anti-aliasing and the perfect reconstruction conditions, and at the same time, they resemble as much as possible the continuous Laguerre wavelets when using the cascade algorithm. We use the mean squared error, the maximum deviation, and the standard deviation to quantify the similarity between the continuous Laguerre wavelets and the constructed discrete Laguerre wavelets. The results show that, they are both the same wavelets due to the small nature of these parameters. Our method is important because, it can permit the determination of the finite impulse response filter coefficients corresponding to many other continuous wavelets.