翻訳と辞書 Words near each other ・ Quadratino ・ Quadrato di Villafranca ・ Quadratojugal bone ・ Quadratrix ・ Quadratrix of Hippias ・ Quadratur des Kreises ・ Quadrature ・ Quadrature (astronomy) ・ Quadrature (mathematics) ・ Quadrature amplitude modulation ・ Quadrature based moment methods ・ Quadrature booster ・ Quadrature division multiple access ・ Quadrature domains ・ Quadrature filter ・ Quadrature mirror filter ・ Quadrature modulation ・ Quadratus ・ Quadratus (martyr) ・ Quadratus femoris muscle ・ Quadratus lumborum muscle ・ Quadratus of Athens ・ Quadratus plantae muscle ・ Quadray coordinates ・ Quadrel ・ Quadrelle ・ Quadrem ・ Quadrennial ・ Quadrennial comprehensive policy review ・ Quadrennial Defense Review Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quadrature mirror filter ： ウィキペディア英語版 Quadrature mirror filter In digital signal processing, a quadrature mirror filter is a filter whose magnitude response is the mirror image around $\backslash pi/2$ of that of another filter. Together these filters are known as the Quadrature Mirror Filter pair. A filter $H\_1(z)$ will be quadrature mirror filter of $H\_0(z)$ if $H\_1(z)\; =\; H\_0(-z)$ The filter responses are symmetric about $\backslash Omega\; =\; \backslash pi\; /\; 2$ :$|H\_1(e^)|\; =\; |H\_0(e^)|$ In audio/voice codecs, a quadrature mirror filter pair is often used to implement a filter bank that splits an input signal into two bands. The resulting high-pass and low-pass signals are often reduced by a factor of 2, giving a critically sampled two-channel representation of the original signal. The analysis filters are often related by the following formulae in addition to quadrate mirror property: :$|H\_0(e^)|^2\; +\; |H\_1(e^)|^2\; =\; 1$ where $\backslash Omega$ is the frequency, and the sampling rate is normalized to $2\backslash pi$. This is known as power complementary property. In other words, the power sum of the high-pass and low-pass filters is equal to 1. Orthogonal wavelets -- the Haar wavelets and related Daubechies wavelets, Coiflets, and some developed by Mallat, are generated by scaling functions which, with the wavelet, satisfy a quadrature mirror filter relationship. ==Further Description== The earliest wavelets were based on expanding a function in terms of rectangular steps, the Haar wavelets. This is usually a poor approximation, whereas Daubechies wavelets are among the simplest but most important families of wavelets. A linear filter that is zero for “smooth” signals, given a record of $N$ points $x\_n$ is defined as: :$y\_n\; =\; \backslash sum\_^\; b\_i\; x\_$ It is desirable to have it vanish for a constant, so taking the order $m\; =\; 4$ for example: :$b\_0\; \backslash centerdot\; 1\; +\; b\_1\; \backslash centerdot\; 1\; +\; b\_2\; \backslash centerdot\; 1\; +\; b\_3\; \backslash centerdot\; 1\; =\; 0$ And to have it vanish for a linear ramp so that: :$b\_0\; \backslash centerdot\; 0\; +\; b\_1\; \backslash centerdot\; 1\; +\; b\_2\; \backslash centerdot\; 2\; +\; b\_3\; \backslash centerdot\; 3\; =\; 0$ A linear filter will vanish for any $x\; =\; \backslash alpha\; n\; +\; \backslash beta$, and this is all that can be done with a fourth order wavelet. Six terms will be needed to vanish a quadratic curve and so on given the other constraints to be included. Next an accompanying filter may be defined as: :$z\_n\; =\; \backslash sum\_^\; c\_i\; x\_$ This filter responds in an exactly opposite manner, being large for smooth signals and small for non-smooth signals. A linear filter is just a convolution of the signal with the filter’s coefficients, so the series of the coefficients is the signal that the filter responds to maximally. Thus, the output of the second filter vanishes when the coefficients of the first one are input into it. The aim is to have: :$\backslash sum\_^\; c\_i\; b\_i\; =\; 0$ Where the associated time series flips the order of the coefficients because the linear filter is a convolution, and so both have the same index in this sum. A pair of filters with this property are defined as quadrature mirror filters.〔 .〕 Even if the two resulting bands have been subsampled by a factor of 2, the relationship between the filters means that approximately perfect reconstruction is possible. That is, the two bands can then be upsampled, filtered again with the same filters and added together, to reproduce the original signal exactly (but with a small delay). (In practical implementations, numeric precision issues in floating-point arithmetic may affect the perfection of the reconstruction.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quadrature mirror filter」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.