Robust, Efficient Design of Allpass Filters for Dispersive String Sound Synthesis
Jonathan S. Abel, Vesa Välimäki, Julius O. Smith · IEEE Signal Processing Letters · 2010
An efficient allpass filter design method is introduced to match the dispersion characteristics of vibrating stiff strings. The proposed method designs an allpass filter in cascaded biquad form directly from the target group delay, placing the poles at frequencies at which the group delay area function achieves odd integer multiples of ¿, and fixing the pole radii according to a smoothness parameter. The pole frequencies are seen to be roots of quartic polynomials, and an efficient approximation to the desired roots is provided. Design examples show the method to outperform a previous closed-form design. Furthermore, the proposed method can achieve an arbitrarily wide bandwidth of good approximation by increasing the filter order, as the method is numerically robust and yields stable allpass filters.