Multi-channel filter bank (MFB) is investigated systematically.A kind of nonsingular multi-channel filter banks (NMFB) is defined.The analysis equations

synthesis equations and transfer equations of NMFB are introduced.And the optimizing restrictions for normalizing

smoothing and symmetry of filters are discussed.Particularly

the concept of zero spectrum moment filters to optimize filter's character is proposed.At last the design procedure and example of symmetric multi-channel filter bank are given.