Design and parallel implementation of FIR digital filters with simultaneously variable magnitude and non-integer phase-delay

Variable fractional-delay digital filters are useful in various signal processing applications. To perform both fractional-delay filtering and signal frequency selecting, variable fractional-delay filters must also have variable magnitude characteristics. This paper proposes a method for designing variable finite-impulse response (FIR) filters with both variable magnitude and variable noninteger phase-delay. First, the coefficients of a variable FIR filter are expressed as different 2-variable polynomials of a pair of spectral parameters; one is for varying magnitude response, and the other is for varying noninteger phase-delay. Then the optimal coefficients of the 2-variable polynomials are found by minimizing the total weighted squared error of the variable frequency response. Since the coefficients of the obtained variable FIR filter are the polynomials of the two spectral parameters, we can yield variable magnitude and variable noninteger phase-delay simultaneously or independently by substituting different spectral parameter values to the 2-variable polynomial coefficients. Finally, we show that the resulting variable FIR filter can be implemented in a parallel form, which is suitable for high-speed signal processing.