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Design of halfband filters for orthonormal wavelets using ripple-pinning

Design of halfband filters for orthonormal wavelets using ripple-pinning

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The design of halfband filters for orthonormal wavelet with a prescribed number of vanishing moment and prescribed ripple amplitudes is described. The technique is an extension of the zero-pinning (ZP) technique and is called ripple-pinning (RP). In ZP, the positions of stopband minima (of a Bernstein polynomial) are specified explicitly and the stopband maxima (position and amplitude) depend implicitly on the minima. In RP, the amplitude of the ripples is explicitly specified and this leads to a set of non-linear (polynomial) equations with the position of both the minima and maxima as unknowns. An iterative algorithm is proposed to solve the equations and design examples will be presented. Two variations of the RP technique, which allow for the transition band sharpness to be explicitly specified, are also presented.

Inspec keywords: band-stop filters; wavelet transforms; iterative methods; nonlinear equations

Other keywords: orthonormal wavelet; stopband minima; ripple-pinning; iterative algorithm; halfband filter design; nonlinear equation; stopband maxima; zero-pinning technique

Subjects: Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Filtering methods in signal processing; Nonlinear and functional equations (numerical analysis); Filters and other networks; Nonlinear and functional equations (numerical analysis); Signal processing theory

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