The main motivation of this work is sound synthesis by use of physical models. Many studies have been undertaken on the modeling of physical systems by means of waveguide filters. These methods consist actually in simulating the propagation of acoustic waves with digital delay lines. These models are constrained to have a spatial step determined by the sampling rate. This is a serious drawback when a high spatial resolution in the geometry of the model is needed or when the length of the waveguide needs to vary. One can use digital filters for approximating the fractional delay, but length variations usually induce audible distortions because of local instabilities or modification in the filter's structure.
In this paper we propose a new point of view for approximating ideal fractional delays which leads to new interpretations for two families of well known approximations: Lagrange Interpolator Filters (LIF) and Thiran Allpass Filters. Both are based on expansions (series expansion and continued fraction expansion) of the analytic extention of the Fourier transform of the impulse response of the ideal fractional delay. In the case of Lagrange Interpolator Filters, this results in a new modular structure which is more efficient for time varying applications. In the case of the allpass filters, this leads to a new modular structure and theoretical model.