Design of Multi-channel Cosine-Modulated Filter Bank Based on Fractional Derivative Constraints Using Cuckoo Search Algorithm

In this work, a hybrid method is proposed for the design of uniform M-channel cosine-modulated banks. This method is based on the combination of a gradient- or slope-based optimization such as Lagrange multiplier method, and nature-inspired optimization technique called cuckoo search optimization. The prototype filter design problem for CM filter bank is formulated in frequency domain as sum of $$L_{2}$$L2 norm of error in passband, stopband and transition band at $$\pi /2M$$π/2M frequency. Lagrange multiplier method is used to derive closed form expression for the optimized filter coefficients using fractional derivative constraints, and cuckoo search optimization technique is used for finding optimal fractional derivative constraints taking peak reconstruction error (PRE) as an overall objective function for M-channel CM filter bank. Performance of the proposed method is evaluated by passband error $$(\phi _\mathrm{p})$$(ϕp), stopband error $$(\phi _\mathrm{s})$$(ϕs), transition band error $$(\phi _\mathrm{t})$$(ϕt), PRE, aliasing error $$(e_\mathrm{a})$$(ea), stopband attenuation $$(A_\mathrm{s})$$(As) and computational time. It was found that the proposed method gives better performance as compared to earlier existing techniques.