image-processingscalingwavelethaar-wavelet

Wavelet Filter and Scaling Function


I am trying to plot the values of a symbol scaled between 0 and 1. The equations that satisfy these elements are as follows:-

h0^2+h1^2+h2^2+h3^2==1
h0*h2+h1*h3==0
h0+h1+h2+h3==sqrt(2)
h0-h1+h2-h3==0
h1-2*h2+3*h3==0

The absolute values of

h0 = ~0.966
h1 = ~1.673
h2 = ~0.448
h3 = ~0.25

The value of h1 is outside 0-1. How do I scale them so that the values are between 0-1.

Further, I need to find the scaling function and plot it.

Thanks for the help.


Solution

  • If you are trying to plot the Daubechies scaling function of order 2 (with 4 coefficients) compare your filter taps to the ones used in this cascade algorithm example and check its output. This is the algorithm that applies the scaling filter (and upsampling) to itself.

    My guess is you are there if you use h3 = -h3 and then divide all your filter taps by sqrt(2).