Patent ID: 7805012

Claim:
A computer-implemented method of signal processing, comprising: receiving a plurality of digitized coefficients; determining a best-fit distribution of a general family of distributions for the plurality of digitized coefficients, the general family of distributions comprising a generalized gamma distribution having at least a first shape parameter, wherein the first shape parameter for the best-fit distribution is determined by obtaining, via one or more iterations, a global root value of a shape estimator equation that utilizes the plurality of digitized coefficients, wherein the iterations are globally-convergent to the global root value irrespective of a starting value of the first shape parameter, the global root value being the first shape parameter of the best-fit distribution; and providing a characterization of the digitized coefficients based upon the determined best-fit distribution, wherein the shape estimator equation is provided by one of ( i ) ⁢ ⁢ S n ⁡ ( β ) := log ⁡ ( M n ⁡ ( 2 ⁢ ⁢ β ) ) - 2 ⁢ ⁢ log ⁡ ( M n ⁡ ( β ) ) - log ⁡ ( 1 + β ⁡ ( R . n ⁡ ( β ) - R . n ⁡ ( 0 ) ) ) = 0 ⁢ ⁢ and ⁢  ⁢ ( i ⁢ ⁢ i ) ⁢ ⁢ T n ⁡ ( β ) := M n ⁡ ( 2 ⁢ ⁢ β ) M n 2 ⁡ ( β ) - ( 1 + β ⁡ ( R . n ⁡ ( β ) - R n ⁡ ( 0 ) ) ) = 0 , ⁢ ⁢ ( i ⁢ ⁢ i ⁢ ⁢ i ) ⁢ ⁢ S n ⁡ ( β ) := log ⁡ ( M n ⁡ ( 2 ⁢ ⁢ β ) ) - 2 ⁢ ⁢ log ⁡ ( M n ⁡ ( β ) ) - log ⁡ ( 1 + 1 λ 0 ) = 0 , and ⁢ ( i ⁢ ⁢ v ) ⁢ ⁢ T n ⁡ ( β ) := M n ⁡ ( 2 ⁢ ⁢ β ) M n 2 ⁡ ( β ) - ( 1 + 1 λ 0 ) = 0 , wherein ⁢ ⁢ M n ⁢ : ⁢ ⁢ t ↦ 1 n ⁢ ∑ i = 1 n ⁢  X i  t , X 1 ⁢ ⁢ … ⁢ ⁢ X n are the digitized coefficients, R . n := M . n M n , M . n denotes a derivative of M n with respect to t, and λ 0 is a known value of an index shape parameter, wherein the prior steps are performed by one or more computers.