A filter structure formed as a linear combination of a bank of nonlinear filters, in particular, as linear combination of a bank of stack filters, is studied. This type of filter includes many known filter classes, e.g., linear FIR filters and nonlinear threshold Boolean filters, L-filters. An efficient algorithm based on joint distribution functions of stack filters for finding optimal filter coefficients under MSE (mean squared error) criterion is proposed. A subclass of the above filters, called FFT-ordered L-filters (FFT-LF), is studied in detail. In this case the bank of filters is formed according to the generalized structure of the FFT flowgraph. It is shown that FFT-LFs effectively remove mixed Gaussian and impulsive noise. Possessing good characteristics of performance, FFT-LFs are simple in implementation. The most complicated (in the sense of implementation) FFT-LFs are well known L-filters. We suggest an efficient parallel architecture implementing FFT-LFs as well as a family of discrete orthogonal transforms including discrete Fourier, Walsh and other transforms. Both linear and nonlinear L-filter-type filters are implemented effectively on the architecture. Comparison with known architectures implementing both linear and nonlinear filters reveals advantages of the proposed architecture.