Many wavelet does not have functional form, but defined by the MRA coefficient.

The visualization of wavelet can be done by using wavelet construction.

For scaling function, we can define and .

Similarly, the wavelet can be started with and .

Then build by iteration,

From last post on the scaling coefficient, i calculated and plot the wavelet for .

we can see the wavelet becomes the Haar wavelet as the free parameter goes to 1. In fact, it becomes a shifted Haar wavelet when the free parameter goes to 0, as we can imagine.

When the free parameter is 0.683013, it is the Daubechies-2 wavelet. Notes that some people will absorbed a factor $latex 1/ \sqrt{2} $ into the coefficient, so that their free parameter is .