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Complementarity, perhaps the most basic principle of quantum mechanics, distinguishes the world of quantum phenomena from the realm of classical physics. Quantum mechanically, one can never expect to measure both precise position and momentum of a quantum at the same time. It is prohibited. We say that the quantum observables “position” and “momentum” are(More)
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)
The condition on scaling filters of two orthogonal wavelet bases that render the corresponding wavelets as Hilbert transform pairs is re-examined in this note. Without making any pre-assumption on the relationship between the two scaling filters, the authors derive necessary and sufficient conditions for forming Hilbert transform pairs. They lead to new(More)
  • Runyi Yu
  • IEEE Transactions on Signal Processing
  • 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 paper studies the structural properties of both 3nite poles and the in3nite pole of linear time-invariant singular systems under output feedback. Three main problems are studied, namely, (1) the algebraic structures of both 3nite poles and the in3nite pole; (2) the assignability of 3nite poles and the elimination of the in3nite pole by output feedback;(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
  • IEEE Transactions on Signal Processing
  • 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)