Vesa Välimäki
Matti Karjalainen
Digital waveguide filters provide an efficient technique for constructing physical models of acoustic systems. They are based on the use of lossless digital waveguides that are simply bi-directional delay lines. Frequency-dependent losses can be included in the model by placing one or more digital lowpass filters in the delay loop. Waveguide modeling has been extensively applied to physical modeling of the human vocal tract and musical instruments. Theoretical foundations of waveguide models have been mainly developed by Dr. Julius Smith at CCRMA, Stanford University.
At the HUT Acoustics Laboratory , we have studied extensions of digital waveguide filters that we call fractional delay waveguide filters (FDWF). Fractional delay (FD) stands for a time delay that is a noninteger multiple of the sampling interval. Fractional delay (FD) stands for a time delay that is a noninteger multiple of the sampling interval. Fractional delays are implemented using digital FIR or IIR filters. In digital waveguide models FDs are needed for two purposes: for adjusting the length of delay lines and for adjusting the position of scattering jucntions between waveguides that have different wave impedance. We have found that classical Lagrange interpolation, which is implemented as an FIR filter, is a good choice for interpolation of audio signals since it is most accurate at low frequencies. Generally speaking, the advantage of FIR-type FD filters is that there are no transients due to a change of parameters (delay) of the filter.
Adjusting the position of a scattering junction in a waveguide model required definition of a new operation: insertion of a discrete-time signal into a point between the samples of a delay line. We call this operation deinterpolation. It is an inverse operation to interpolation but in a different sense than inverse interpolation or decimation. Nonrecursive deinterpolation is implemented using the transpose FIR filter structure. The coefficients of this filter are the same as those of the corresponding interpolating filter but they are in the time-reversed order.
Using interpolation and deinterpolation we have developed a new kind of model for the human vocal tract. In this model, the length of each tube section is not anymore restricted by the sampling interval but it can be arbitrary. The control of the model is simplified because each tube section can be associated with a certain part of the vocal tract. For example, the movement of the tongue is easily simulated by changing the diameter and locations of the end points (scattering junctions) of the corresponding section in the fractional delay tube model.
Vesa Välimäki, Matti Karjalainen, and Timo Kuisma. Articulatory control of a vocal tract model based on fractional delay waveguide filters. In Proc. 1994 Int. Symp. Speech, Image Processing and Neural Networks (ISSIPNN'94), vol. 2, Hong Kong, April 13-16, 1994, pp. 571-574.
Vesa Välimäki, Matti Karjalainen, and Timo Kuisma. Articulatory speech synthesis based on fractional delay waveguide filters. In Proc. 1994 IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP'94), vol. 1, Adelaide, Australia, April 19-22, 1994, pp. I-585 - I-588.
Vesa Välimäki, Fractional Delay Waveguide Modeling of Acoustic Tubes. Licentiate's thesis. Report no. 34, Helsinki University of Technology, Faculty of Electrical Engineering, Laboratory of Acoustics and Audio Signal Processsing, Espoo, Finland, July 1994, 133 p.