小波分析信號處理(matlab)

1、123 is a set, if aS and bS a+bS ( (or ), aSS We call a linear space. SRCaS加法滿足對稱性、交換律和結(jié)合律）（數(shù)乘滿足結(jié)合律和分配律，有0元）Y=kx與y=kx+b4 is a linear space on number domain R or C, for each a norm function is defined. A non-negative function|is called a norm function if and only if ,( ) 1. | | 0, | | 00 2. XxXx yXR C

2、xxx，| | 3. | |xyxyxx絕對值=模=長度=距離=范數(shù)5n12222ba22Euclidean space R S= ,| , , is a set of functions , ( )| ( )| =( ) ( ):(),| ,nkkkbakkkkx xxxCx yx yL a bL a bx tx tdtx t y t dtlxkzxx yx y 6A Hilbert Space is a linear space X equipped with a dot productwhich is also called inner product. A function (real

3、 or complex) is a inner product () if and only if for , , and a,bC1. ,x y zXx內(nèi)積,;2. , 0, and ,00;3. , and ,4. ,Define a norm: | |=, under which X is complete.yy xx xx xxax yax yx ayax yxy zx zy zxx x 7If ,0, we say and is orthogonal. Denoted by A is a subset of Hilbert space X, , yA,0, we say that i

4、s orthogonal to set A. Denoted by and are two subsets of , if andx yxyxyxXx yxxAABXxA , we have , we say and are orthogonal to each other. Denoted byyBxyABAB8 is a subset of Hilbert space , if for different and ,0, we call a orthogonal system.If ,1, is called a standard orthogonal system () also cal

5、led orthonormal system.kjkjkkjjkxXxxxxxxxx標(biāo)準(zhǔn)正交系 ，9 is a subset of Hilbert space , if1. , where are numbers2. 00We say that is a basis of .If is orthogonal system, we say that is a orthogonal basis of kkkkkkkkkkxXxX xc xcc xcxXxxX 10 and are two subspaces of Hilbert space ,:|,We say that C is the sum

6、 of A and B. Additionally, if, we say C is the direct sum of A and B, denoted by and are complemetary ABXCABxy xA yBABCABABin , ,C BAAB111213141516172. f(t) 的頻譜（線頻譜） f(t)分解為傅氏級數(shù)后包含哪些頻率分量和各分量所占“比重”用長度與各次諧波振幅大小相對應(yīng)的線段進(jìn)行表示，并按頻率的高低把它們依次排列起來所得到的圖形，稱為 f(t) 的頻譜。 幅度頻譜：表示出各諧波分量的振幅。相位頻譜：把各次諧波的初相用相應(yīng)的線段依次排列得到。18

7、)()()()(kjXkXnxFFTkXIR)(nx)()(kjekX)()()(22kXkXkXIR幅度譜：)()()(kXkXarctgkRI相位譜：19()( )jj nnX ex n e1( )()2jj nx nX eed20圖17-8 當(dāng)T=2,5,10時周期矩形波的頻譜)(tfT2t20T121222NFffNss2FfNs2/, 1 , 0NkkNffskNTfNtsp/ptF/123242526tFtftd)(e21)(-idt)(e)(-itfFtnnCtfinte)(27小波基D小波基A原始信號小波系數(shù)wd小波系數(shù)wa正變換：原始信號在小波基上，獲得 “小波系數(shù)”分量反變換：所有“小波分解” 合成原始信號 例如： 小波分解 a=小波系數(shù) wa 小波基A28傅里葉變換(Fourier)基小波基時間采樣基293031 2101200A nested spaces and function () is called a Multiresolution Analysis if they satisefy the following condition:1. 2. ( ), 03. ( )(2 )4. ( )()jjjiiVVVVVVL RVf tVftVf tVf tn00,5. there exis