Does the wavelet toolbox have a function to extract the approximation filter kernels for a specified level?

I would like to have the filter kernel for say, the level 6 approximation (A6) so that I can perform convolution filtering of some signal in another application, like Excel. Is there a function in the wavelet tool box that will give me the kernel directly?

If I use the code below with a 315 sample raw signal Raw, the vector scaleA2 should be the kernel for the level 2 approximation.

   load sym4;

   [Ld Hd Lr Hr]=orthfilt(sym4);

   scaleA2=conv(conv(conv(Ld,dyadup(Ld,0)),dyadup(Lr,0)),Lr);

   scaleA2=scaleA2/norm(scaleA2)/2;

When I convolve it with the raw signal using

   fltr=wkeep(conv(Raw,scaleA2),315);

and compare fltr to A2 produced from

   [C,L]=wavedec(Raw,5,'sym4');

   A2=wrcoef('a',C,L,'sym4',2);

The two are close, but different. What's up???

[Wayne King]

Will you say "filter kernel" here, I assume you mean the filter impulse response. So you given an FIR scaling filter, h(n), you would like to know how to obtain the scaling filter at a specified level. Is that correct?

Answer 1

[Wayne King]

I'm not sure why you are trying to use the synthesis filter here. That does not give you the equivalent filter for the scaling or wavelet filter at a given level of resolution.

The synthesis filter is used for aliasing cancellation and ultimately yields a vector projection onto a particular subspace.

You can get the equivalent filter you want this way:

 [h,~] = wfilters('sym4');
 L = 6;
 %%Using the multirate noble identities
 tmp = h;
 for k = 1:L-1
    tmp = dyadup(tmp,0);
    h = conv(h,tmp);
    h = 1/sqrt(2)*h;
 end

 %%Look at the frequency response
 % Compare the frequency response of the scaling filter and
 % the equivalent frequency response at level 6.

 [LoD,~] = wfilters('sym4');
 Horig = fft(LoD,1024);
 Horig = Horig(1:1024/2+1);
 Hfinal = fft(h,1024);
 Hfinal = Hfinal(1:1024/2+1);
 W = 0:(2*pi)/1024:pi;
 plot(W,abs(Horig),'r','linewidth',2);
 hold on;
 plot(W,abs(Hfinal))
 legend('Scaling filter','Equivalent filter at level 6');
 set(gca,'xtick',[pi/2^L pi/2 pi]);
 xlabel('Radians/sample');
 grid on;

 % Zoom in on the frequency response of the level-6 equivalent filter

 figure;
 plot(W,abs(Hfinal))
 set(gca,'xlim',[0 pi/2^(L-2)]);
 set(gca,'xtick',[pi/2^L pi/2^(L-1)])
 xlabel('Radians/sample');
 grid on;
 title('Equivalent Scaling Filter at Level 6');