  This work characterizes (dyadic) wavelet frames for $L^2({\mathbb R})$ by
means of spectral techniques. These techniques use decomposability properties
of the frame operator in spectral representations associated to the dilation
operator. The approach is closely related to usual Fourier domain fiberization
techniques, dual Gramian analysis and extension principles, which are described
here on the basis of the periodized Fourier transform. In a second paper of
this series, we shall show how the spectral formulas obtained here permit us to
calculate all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed
number of generators of minimal support.
