  Utilizing the Haar transform, we study the higher order spectral properties
of mean field avalanche models, whose avalanche dynamics are described by
Poisson statistics at a critical point or critical depinning transition. The
Haar transform allows us to obtain a time series of noise powers, $H(f_1,t)$,
that gives improved time resolution over the Fourier transform. Using
$H(f_1,t)$ we analytically calculate the Haar power spectrum, the real 1.5
spectra, the second spectra, and the real cross second spectra in mean field
avalanche models. We verify our theoretical results with the numerical results
from a simulation of the T=0 mean field nonequilibrium random field Ising model
(RFIM). We also extend our higher order spectra calculation to data obtained
from a numerical simulation of the T=0 infinite range RFIM for $d=3$, and
experimental data obtained from an amorphous alloy, $Fe_{21}Co_{64}B_{15}$. We
compare the results and obtain novel exponents.
