Designing FIR filters in a new vector space

It is pointed out that the time and frequency response of an FIR (finite-impulse response) filter are vectors mapped by the DFT (discrete Fourier transform) matrix. A vector space can be defined by expressing the DFT matrix in terms of the filter as a vector adjacent to the characteristic value matrix. For linear-phase filters, all operations and characteristic values are real, and design constraints in the time and frequency methods are given for computing the orthogonalized characteristic vector matrix, which is used in transforming the design constraints and in computing the filter weights. The procedure is efficient enough to be useful on personal computers