Daubechies wavelet - scaling and wavelet function in MATLAB

[sugaku]

Hi everybody,

I'm trying to reproduce daubechies basic building graph and daubechies wavelet function graph (φ(r)=0 if r≦0 or 3≦r). And i found this algorithm. I would appreciate if there is anybody could help me to understand the function defined below as function [s,w] = cascade(n,cs,cw). Especially how does the convolution takes place. Thank you in advance.

>%Filter coefficients for daub4 (h<->scaling, g<->wavelet)
>h = [1+sqrt(3) 3+sqrt(3) 3-sqrt(3) 1-sqrt(3)]/(4*sqrt(2));
>g = [h(4) -h(3) h(2) -h(1)];
>
>%Calculate 5 iterations of the cascade algorithm
>[s,w]=cascade(5,h,g);

>plot(s); %Plot scaling function
>plot(w); %Plot wavelet function

-----------------------------------------------------------
>function [s,w] = cascade(n,cs,cw)
>
> s = cs;
> w = cw;
> x2(1:2:length(w)*2) = w;
> x2(2:2:end)=0;
> x(1:2:length(s)*2) = s;
> x(2:2:end)=0;
>
> for i = 1:n
>
> s = conv(x,cs);
> w = conv(x2,cs);
>
> x2(1:2:length(w)*2) = w;
> x2(2:2:end)=0;
> x(1:2:length(s)*2) = s;
> x(2:2:end)=0;
>
> end
>
>end

 

[matematikawan]

Probably The MathWorks help is useful.


http://www.mathworks.com/access/hel...convolution&btnG=Google+Search&meta=&aq=f&oq=

 

[oswaler]

I understand your interest in reproducing the Daubechies wavelet function and its scaling function in MATLAB. The algorithm you have provided seems to be a cascade algorithm, which is a common method for constructing wavelet functions. In this algorithm, the convolution takes place by multiplying and summing the input signal with the filter coefficients. This process is repeated for a certain number of iterations, n, to create a more refined wavelet function.

The filter coefficients for the Daubechies wavelet function are provided in the code as h and g, where h represents the scaling coefficients and g represents the wavelet coefficients. These coefficients are used in the convolution process to generate the wavelet function and its scaling function.

I would suggest looking into the mathematical principles behind wavelet functions and convolution to better understand the algorithm. Additionally, there are various resources available online that explain the Daubechies wavelet function and its implementation in MATLAB in more detail.

I hope this helps in your understanding of the function and its implementation. Best of luck in your research.