Patent ID: 7242710

Claim:
A method for reduction of aliasing emerging from modifications of spectral coefficients or subband signals obtained from a digital filterbank, comprising: providing a symmetric low-pass prototype filter p 0 (n), having filter order N; building an M-channel filterbank by complex-exponential modulation of said prototype filter; where said filter has analysis and synthesis filter coefficients based on h k ⁢ ( n ) = p 0 ⁢ ( n ) ⁢ exp ⁢ { ⅈ ⁢ π 2 ⁢ M ⁢ ( 2 ⁢ k + 1 ) ⁢ ( n - N 2 ) } , and n=0 . . . N, and k=0 . . . M−1; filtering a real-valued time domain signal through an analysis part of said filterbank; modifying complex-valued subband signals obtained from said filtering; filtering said modified complex-valued subband signals through the synthesis part of said filterbank; and taking the real part of a complex-valued time domain output signal, where said output signal is a sum of the signals obtained from said synthesis filtering; wherein said optimization of said low-pass prototype filter is accomplished by minimizing a composite objective function ε tot (α) as ε tot (α)=αε t +(1−α)ε a where α is a weighting constant, ε t is the passband error and ε a is the aliasing error; and wherein said passband error ε t is calculated as ɛ t = 1 4 ⁢ π ⁢ ∫ - π π ⁢ ( | A 0 ⁢ ( ⅇ jω ) + A 0 * ⁢ ( ⅇ - jω ) | 2 ⁢ M - 1 ) 2 ⁢ ⅆ ω , and said aliasing error ε a is calculated as ɛ a = 1 8 ⁢ π ⁢ ⁢ M 2 ⁢ ∫ - π π | A M 2 ⁡ ( ⅇ jω ) + A M 2 * ⁡ ( ⅇ - jω ) ⁢ | 2 ⁢ ⁢ ⅆ ω + 1 4 ⁢ π ⁢ ⁢ M 2 ⁢ ∑ l = 1 M 2 - 1 ⁢ ∫ - π π | ⁢ A l ⁡ ( ⅇ jω ) + A M - l * ⁡ ( ⅇ - jω ) ⁢ | 2 ⁢ ⅆ ω where A l (e jω ), l=0 . . . M/2, are the alias gain terms evaluated on the unit circle.