Least mean squared error-design of complex FIR filters with quantized coefficients

The design of complex finite-impulse response filters with quantized coefficients according to a discrete mean squared error (MSE) criterion in the frequency domain is revisited. In the first approach, the coefficients are quantized step-by-step by recursively solving a system of linear equations. The second approach is a generalized form of the first one: The MSE is repeatedly minimized considering a growing number of fixed, quantized coefficients. The first approach requires the same computational burden as the design of unquantized coefficients, in contrast to the second where the higher flexibility is paid with a higher expenditure. For a considerable number of test cases the first approach and one variant of the second achieves a smaller MSE than the direct quantization method.