Wavelet Transforms Generated by splines
نویسندگان
چکیده
In this paper we design a new family of biorthogonal wavelet transforms that are based on polynomial and discrete splines. The wavelet transforms are constructed via lifting steps, where the prediction and update filters are derived from various types of interpolatory and quasi-interpolatory splines. The transforms use finite and infinite impulse response (IIR) filters and are implemented in a fast lifting mode. We analyze properties of the generated scaling functions and wavelets. In the case when the prediction filter is derived from a polynomial interpolatory spline of even order the synthesis scaling function and wavelet are splines of the same order. We formulate conditions for the IIR filter to generate an exponentially decaying scaling function.
منابع مشابه
Advances in Signal Transforms Theory and Applications
Contents Preface ix 1. Wavelet and frame transforms originated from continuous and discrete splines, Amir Z. Averbuch and Valery A. Zheludev 1 1.1. Introduction 1 1.2. Preliminaries 4 1.3. Prediction filters originated from splines 9 1.4. Biorthogonal wavelet transforms generated by filter banks with downsampling factor N = 2 (diadic transforms) 17 1.5. Application of spline-based wavelet trans...
متن کاملOn transformations between Gabor frames and wavelet frames
We describe a procedure that enables us to construct dual pairs of wavelet frames from certain dual pairs of Gabor frames. Applying the construction to Gabor frames generated by appropriate exponential Bsplines gives wavelet frames generated by functions whose Fourier transforms are compactly supported splines with geometrically distributed knot sequences. There is also a reverse transform, whi...
متن کاملFrom Dual Pairs of Gabor Frames to Dual Pairs of Wavelet Frames and vice Versa Ole Christensen and Say
We discuss an elementary procedure that allows us to construct dual pairs of wavelet frames based on certain dual pairs of Gabor frames and vice versa. The construction preserves tightness of the involved frames. Starting with Gabor frames generated by characteristic functions the construction leads to a class of tight wavelet frames that include the Shannon (orthonormal) wavelet, and applying ...
متن کاملSplines: a new contribution to wavelet analysis
We present a new approach to the construction of biorthogonal wavelet transforms using polynomial splines. The construction is performed in a “lifting” manner and we use interpolatory, as well as local quasi-interpolatory and smoothing splines as predicting aggregates in this scheme. The transforms contain some scalar control parameters which enable their flexible tuning in either time or frequ...
متن کاملInterpolatory biorthogonal multiwavelet transforms based on Hermite splines
We present new multiwavelet transforms for discrete signals. The transforms are implemented in two phases: 1. Pre (post)processing which transform the scalar signal into the vector one (and back). 2.Wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform. We p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IJWMIP
دوره 5 شماره
صفحات -
تاریخ انتشار 2007