On the evaluation of the Fourier series coefficients in the design of digital FIR filters

In the design of FIR digital filters by the windowing technique, the unwindowed Fourier series coefficients are required. In practice, however, it is often difficult to evaluate these coefficients. In this paper, we propose two computational procedures to calculate the unwindowed Fourier series coefficients. Their analytic formulas are derived; their computational implementations are discussed; and the practical computation results demonstrate the efficiency of the procedures proposed.