On the design and implementation of FIR and IIR digital filters with variable frequency characteristics

This paper studies the design and implementation of FIR and IIR VDFs, whose frequency characteristics can be controlled continuously by some control or tuning parameters. A least squares (LS) approach is proposed to design FIR VDFs with the impulse response expressed as a linear combination of basis functions. By choosing the basis functions as piecewise polynomials, VDFs with larger tuning range than the ordinary polynomial based approach result. These VDFs can be efficiently implemented using the Farrow structure. Making use of the FIR VDF, an eigensystem realization algorithm (ERA)-based model reduction technique is proposed to obtain a stable IIR VDF with lower system order. It does not suffer from the undesirable transient response during parameter tuning. For frequency selective VDF, about 40% of the multiplications can be saved using the IIR VDF. The implementation of the proposed FIR VDF using the SOPOT coefficients and the multiplier block technique is also studied. Results show that about two-thirds of the additions in implementing the SOPOT coefficients can be saved using the multiplier block.