Wavelets and Filter Banks1_2009课件.ppt

Wavelets and Filter Banks小波与滤波器组;参考书 Wavelet and filter banks, G. Strang, T. Nguyen, Wellesley-Cambridge Press, 1997 （据说有翻译版，也有MIT的ppt 中文有翻译，也可参考瑞士联邦工学院M. Vetterlli的ppt） 多抽样率信号处理，宗孔德，清华大学出版社，1996。 Multirate systems and filter banks, Vaidyanathan, PP., Englewood Cliffs, New Jersey, Prentice Hall Inc. 1993. A wavelet tour of signal processing, S. Mallat, Academic Press. NY, 1998 Ten Lectures on Wavelets, Ingrid Daubechies, 1992 Matlab 6.5, M.;Background needed;课程名称解释;Contents （课程目录）;Contents (cont.);Contents (cont.);Contents (cont.);信号处理基础;捆语祁热卓乍历档轴刹楼尤厂翼私妮艰灵莉竞娟投仗梢沉串盒用锻挝蛛外Wavelets and Filter Banks1_2009课件Wavelets and Filter Banks1_2009课件;Continuous Fourier Transform（连续Fourier 变换） Some basic properties: Linearity （线性性） Parseval Identity: ???Parseval 等式）;Inner product （内积） F_1 and F_2 are two functions in L_2, the inner product of these two functions is defined as: Orthogonality （正交性） If F_1, F_2=0, we say they are orthogonal.;Biorthogonality （双正交性） Two sets of function {F_j} and {G_j}, if F_j, G_k=1 if j=k and 0 otherwise. We call the two set of functions are biorthogonal. Compact support （紧支撑） For a given function f, supp(f)={x|f(x) is not 0} If measure(supp(f)) is finite, we say f is compactly supported or f has compact support. Corresponding to FIR;Basis and frames （基和框架） Basis: unique representation; linear independence（线性独立） and completeness（完备） Frame: linear dependence and completeness but stable Riesz basis: stable basis ;Z transform （Z-变换） ;Lowpass Filter（低通滤波器）=moving average=passing low frequency h={h(n)}, if sum of h is not zero, we call it a lowpass filter, in most time, the sum of h is 1. H(z), H(1)=1 Example: Simplest: H={1 1}/2; (average) Spline: {1 2 1}/4 General: {h(n)} Previous figure Highpass Filter（高通滤波器）=moving difference=passing high frequency;h={h(n)}, is called highpass filter is the sum of h is zero. H(z), H(1)=0 Examples: Simplest: h={1 –1}/2, difference Dual spline: {-1 2 –1}/4; General:{h(n)} sum of h is 0. Figure,x as before, h={-1 2 –1