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The forming of Hilbert transform pairs of biorthogonal wavelet bases of two-band filter banks is studied in this paper. We first derive necessary and sufficient conditions on the scaling filters that render two Hilbert transform pairs: one decomposition pair and one reconstruction pair. We show that the Hilbert transform pairs are achieved if and only if(More)
  • Runyi Yu
  • 2008
We study analyticity of the complex wavelets in Kingsbury's dual-tree wavelet transform. A notion of scaling transformation function that defines the relationship between the primal and dual scaling functions is introduced and studied in detail. The analyticity property is examined and dealt with via the transformation function. We separate analyticity from(More)
This letter is concerned with design of halfband product filters for orthogonal wavelets. We first remark that the recent zero-pinning technique for orthogonal wavelet design cannot always guarantee the nonnegativity of the filter. We then propose to use sum of squares (SOS) decomposition to ensure its nonnegativity. The use of SOS decomposition also allows(More)
  • Runyi Yu
  • 2012
This paper is concerned with quantifying shift-variance of linear systems with continuous-time input and discrete-time output. We first introduce a notion of -shift-invariance for the system. It specifies how the system should respond when the input signal is shifted. For generalized sampling processes, the property is characterized by the sampling kernel,(More)
We certify that we have read this thesis and that in our opinion it is fully adequate in scope and quality as a thesis for the degree of Master of Science in Electrical and Electronic Engineering. ABSTRACT For the application of UPS inverters. The aim of the UPS is to provide the necessary loads with a sinusoidal output voltage at low harmonic distortion.(More)
This paper studies the structural properties of both ÿnite poles and the inÿnite pole of linear time-invariant singular systems under output feedback. Three main problems are studied, namely, (1) the algebraic structures of both ÿnite poles and the inÿnite pole; (2) the assignability of ÿnite poles and the elimination of the inÿnite pole by output feedback;(More)
This paper introduces a recently designed dual-tree complex wavelet and studies its application in image denoising. The primal filter bank is selected to be the Daubechies 9/7 filter bank, and the dual filter bank is designed to have length of 10/8; both filter banks are biorthogonal and symmetric. The wavelets of the dual-tree filter bank form (almost)(More)