Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the Villemoes machine is used to compute the Sobolev smoothness of a refinable function, which involves the computation of the spectral radius of a special matrix which has at least quadratic time complexity with respect to the refinement mask size.
17 citations
TL;DR: In this paper, a lattice structure of biorthogonal linear-phase filter banks (BOLPFBs) using new building blocks which can obtain long filters with fewer number of building blocks than conventional ones is proposed.
Abstract: This paper proposes a lattice structure of biorthogonal linear-phase filter banks (BOLPFBs) using new building blocks which can obtain long filters with fewer number of building blocks than conventional ones. The structure is derived from a generalization of the building blocks of first-order LPFBs. Furthermore, the proposed building blocks are applicable for both even and odd number of channels. The resulting FBs have good performance in stopband attenuation and low implementation costs.
17 citations
Patent•
20 Nov 2013
TL;DR: In this article, an integral coding/decoding method based on MIMO radar communication is proposed, which guarantees the orthogonality of bipolar phase spread spectrum code sequence based on WalsH matrix.
Abstract: The invention provides an integral coding/decoding method based on MIMO radar communication. The orthogonal spread spectrum code sequence guarantees the orthogonality of bipolar phase spread spectrum code sequence based on WalsH matrix. The requirement of the radar to the detection of signal self-correlation peak value, mutual correlation peak value low side-lobe can be satisfied through the genetic algorithm. The signal encoding is based on soft spread spectrum biorthogonal encoding. To satisfy the requirement of the MIMO radar to detection signal, different spreading coding sequences can be used on different encode element positions; special sending channel can be reserved as the time and frequency synchronous standard, the first encode element position of each sending channel is reserved as the phase position standard, and special synchronous spreading codes are used on the positions. According to the method provided by the invention, conventional carrier frequency offset extraction technology, carrier phase partial extraction technology and soft spread spectrum biorthogonal decoding method are improved specifically according to the requirement of the radar/radio frequency integrate realization, accompanied by the frequency offset tracking technology with Alpha -Beta as the core, accuracy of data deviation correction is guaranteed.
17 citations
TL;DR: Two generalizations of the original construction of Malvar, Coifman, and Meyer are presented: biorthogonal and equal parity bases, which have the advantage that constant and linear components, respectively, can be represented efficiently.
Abstract: We discuss smooth local trigonometric bases and their applications to signal compression. In image compression, these bases can
reduce the blocking effect that occurs in the Joint Photographic Experts Group (JPEG). We present and compare two generalizations of the original construction of Malvar, Coifman, and Meyer: biorthogonal and equal parity bases. These have the advantage that constant and linear components, respectively, can be represented efficiently. We show how they reduce blocking effects and improve the SNR.
17 citations
TL;DR: The proposed scheme is based on interpolation, and as such, it involves only samples of signals, and it does not require any use of quadrature formulas.
Abstract: We present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction, we used the interpolatory discrete splines, which enabled us to design a library of perfect reconstruction filterbanks. These filterbanks are related to Butterworth filters. The construction is performed in a "lifting" manner. The difference from the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform (FFT). Two ways to choose the control filters are suggested. The proposed scheme is based on interpolation, and as such, it involves only samples of signals, and it does not require any use of quadrature formulas. These filters have a linear-phase property, and the basic waveforms are symmetric. In addition, these filters yield refined frequency resolution.
17 citations