Optimization of filter banks using cyclostationary spectral analysis

Generally, the output of a filter bank for a stationary input signal is not stationary but cyclostationary. In this paper, by using cyclostationary spectral analysis, the spectral correlation density of this output is derived. Using this result we derive a criterion to construct an optimal 2-band perfect reconstruction filter bank which minimizes the averaged mean squared reconstruction error when the high pass band signal is dropped. By adding constrains to the filter coefficients, the biorthogonal filter bank, the conjugate quadrature filter bank and the biorthogonal linear phase filter bank are respectively obtained. Some numerical results are also presented for optimal biorthogonal and PR linear phase filter banks which are compared in terms of some performance measures