This invention relates to the field of filter technology, and particularly to a design method,
system, device, and medium for a quasi-completely reconstructed
filter bank. The method first uses a generalized monotonic asymptotically saturated function as the initial value of a
prototype filter, substituting it into the
filter bank model for optimization to obtain a baseline fully reconstructed
prototype filter. Then, a
transition band adjustment parameter is introduced to perform an analytical mapping transformation on the amplitude-
frequency response of the baseline fully reconstructed
prototype filter, resulting in a fully reconstructed prototype filter with optimized
transition band. Finally, combined with a determined number of
filter bank channels and the
polyphase decomposition length of the prototype filter, a quasi-completely reconstructed prototype filter is obtained through
frequency domain sampling and transformation
processing, which is then modulated to obtain a quasi-completely reconstructed filter
bank. This method, by introducing a generalized monotonic asymptotically saturated function as the initial value of the prototype filter and combining it with the analytical mapping mechanism of the
transition band adjustment parameter, significantly improves
stopband attenuation performance and increases the efficiency of prototype filter coefficient generation while ensuring quasi-complete reconstruction.