傳立叶变换与小破变换 IFT: f(x) F(oe d 2丌 TWT: f(x)=W,(a, b)vab(x)db 1 x-b v()
傅立叶变换与小波变换 1 ( ) ( ) 2 j x f x F e d − = ( ) 1 ( ) ( , ) ( ) 1 ( ) , 0 , 2 a x b a x a da W a b x db C f x a b f a b − = = − IFT: IWT:
傳立叶变换与小破变换 . FT: F(o)= f(x)e Joxdx BWT: W,(a, b)=f(xva, b (x)dx
傅立叶变换与小波变换 ( ) ( ) j x F f x e dx − − = − W a b = f x x dx f a b ( , ) ( ) ( ) , FT: WT:
回区 File Edit Yiew Go Web Window Hell 回ν+昌 Find in page Wavelet Toolbox Wavelets:A New Tool for Signal Analysis: The Continuous Wavelet Transform dd to Favorites The Continuous wavelet Transform C(scale, position)=I f(t)y(scale, position, t)dt The result of the Cwt are many wavelet coefficients C, which are a function of scale and position Multiplying each coefficient by the appropriately scaled and shifted wavelet yields the constituent wavelets of the original signal Wavelet rainstorm gnd Constituent wavelets of different scales and positions Number of dimension Scaling
The Continuous Wavelet Transform
) Help ri1 e Edit View Go Web置 indow且e1p Find in page Wavelet Toolbox Wavelets: A New Tool for Signal Analysis: Scaling 7 Add to Favorites Wavelet Toolbox Scaling We've already alluded to the fact that wavelet analysis produces a time-scale view of a signal, and now we re talking about scaling and shifting wavelets. What exact do we mean by scale in this context? Scaling a wavelet simply means stretching (or compressing) it To go beyond colloquial descriptions such as"stretching we introduce the scale factor, often denoted by the letter a. If we're talking about sinusoids, for example, the effect of the scale factor is very easy to see f(t)= sin(t) f(t=sin C f(t)=sin(t);a= I f(t)=sin(4t)ia= I
( ) a t f (t) = sin
) Help ri1 e Edit View Go Web置 indow且e1p Find in Wavelet Toolbox Wavelets: A New Tool for Signal Analysis: Scaling 7 Add to Favorites Scaling f(t)=y(t) 1“n12 f()=叭Va f(t)=甲(2t) f(t)= y(4t);a It is clear from the diagrams that, for a sinusoid sin(ot), the scale factor a is related (inversely) to the radian frequency o. Similarly, with wavelet analysis, the scale is related to the frequency of the signal We 'll return to this topic later. The continuous wavelet transform Shifting
Scaling ( ) a t f (t) =