Two-channel orthogonal mirror image filter bank design method based on iterative gradient search
A gradient search, filter bank technology, applied in impedance networks, digital technology networks, electrical components, etc., can solve problems such as the absence of matrix inversion, high filter length, and expression of minimization and maximization.
Active Publication Date: 2019-07-26
HANGZHOU DIANZI UNIV
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However, since the prototype filter coefficients of this method are directly obtained by calculating the equation composed of approximate matrix inversion and matrix multiplication, the matrix inversion itself has a high computational complexity. In addition, due to the length of the filter High, it may also lead to the situation that there is no matrix inverse
[0004] Since the optimization process of the analytical solution cannot directly express the minimum-maximization form, in the existing design methods, in order to obtain the QMFB with ripple characteristics such as reconstruction error or stop-band attenuation, WLS or improved The WLS method, rather than directly based on the minimum-maximization criterion to obtain
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[0063] The present invention will be further described below in conjunction with accompanying drawing.
[0064] Such as figure 1 As shown, the specific steps of the two-channel orthogonal mirror filter bank design method based on iterative gradient search are as follows:
[0065] Step 1. According to the design requirements, determine the number of frequency points L on the full frequency band, the linear phase prototype filter (usually we also use the low-pass analysis filter H 0 (w) is called the prototype filter) order N (order N is an even number), stop band cut-off frequency fs.
[0066] Determine the full frequency matrix U of the low-pass filter by formulas (1a), (1b), and (1c) respectively t , stopband frequency matrix U s and high-pass filter full-frequency matrix U t，(w+π) .
[0067] u t =[c(w 1 ),...,c(w s ),...,c(w L )] T (1a)
[0068] u s =[c(w s ),c(w s+1 ),...,c(w L )] T (1b)
[0069] u t，(w+π) =[c(w 1 +π),...,c(w s +π),...,c(w L +π)] T ...
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The invention provides a two-channel orthogonal mirror image filter bank design method based on iterative gradient search. According to the method, an original high-nonlinearity non-convex optimization problem is converted into a convex optimization problem to be iteratively solved by utilizing an iterative gradient search (IGS) technology. Compared with the prior art, the method provided by the invention is not limited to solving a certain fixed objective function any more, and the objective function can be flexibly changed according to the design requirement, so that the objective function can be expressed in the form of a least square criterion, and the expression form of the least square criterion can be directly realized. Compared with other methods at home and abroad, the method hasthe advantages that the normal selection of the iteration initial coefficient of the prototype filter hardly affects the simulation result, and the obtained filter performance index is more superior.
Description
technical field [0001] The invention belongs to the technical field of digital signal processing, and in particular relates to a design method for a two-channel orthogonal mirror filter bank based on iterative gradient search technology. Background technique [0002] In recent years, two-channel quadrature mirror filter bank (QMFB, quadrature mirror filter bank) has been applied in more and more fields, such as sub-band coding of speech and image signals, wavelet base design, etc. Due to the wide application of QMFB, people pay more and more attention to its design. There are many design methods of QMFB with LP and NPR characteristics that have been proposed, all of which can be regarded as design methods based on the least square criterion and the minimum maximization criterion. [0003] The most traditional design method is Johnston's method. He proposed to use the weighted sum of reconstruction error energy and stop band energy as the objective function and use the Hooke...
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IPC IPC(8): H03H17/02
CPCH03H17/0272
Inventor 王浩赵晨子赵知劲李伟琪李祥振
Owner HANGZHOU DIANZI UNIV