Frequency Domain Optimization Design of Linear Phase Cosine Modulated Filter Banks

The modulated filter´s properties are mainly decided by the prototype filter properties, so the key to the modulated filter banks design is to obtain a prototype filter which has good stopband attenuation performance. In frequency domain, a simple and effective design method is introduced. According to the frequency sampling technology, the proposed method takes the stopband attenuation as a target function, designs the linear phase prototype lowpass filter by combining Lagrange polynomial approximation with particle swarm optimization. And then, the analysis and synthesis filters can be obtained by using 2M channels of cosine modulation. Theoretical analysis and experimental results show that modulated subband filters all have linear phase when N (filter order) and M (channel number) is meet to the expression as N=2m₀M+1 (m₀ may be any integer), and the filter banks have better stopband attenuation and reconstruction performance than others.