Any multiresolution analysis gives rise to a wavelet basis. The converse is not true: a wavelet basis does not necessarily come from a multiresolution analysis (Mallat).

Haar wavelet

This is the simplest non-trivial wavelet, g(x) is +1 on [0,1/2] and -1 on [1/2,1] It does not give an unconditional basis in spaces other than L².

Meyer wavelet

The Meyer wavelet has the support of g^ in |v| in [2/3 π, 8/3 π].

Franklin wavelet

Let D_a be the triangle function with support [0,1-|a|], i.e., D_a(x)= 1 - |x| / a. Notice that D_a=X_[0,A] * X_[0,A].

Consider the subspace, V₀, of L² spanned by the dilates D_a-k. If F belongs to this subspace, F=∑_k F_k D_a-k, has Fourier transform F^(v) = [sin(π v)/π v]² m_F(v) where m_F(v) = ∑ F_k exp(-2 π i k v) is periodic with period 1.

To find the Franklin wavelet we have to find an orthonormal basis of V₀. We can write h^ in the above form and the orthonormality condition requires (up to a phase which is set to zero),

The wavelet g that minimizes Int (x-1/2)² |g(x)|² is,

where |K|=1. g belongs to V₁.

Daubechies wavelets

Spline wavelets