An all-zero model for higher pole correction

The higher pole correction (HPC) function in relation to the all-pole modelling of the vocal tract transmission is analyzed. A set of theoretical HPC curves for vocal tracts of different effective lengths are calculated. An all-zero model for HPC is proposed. This model is derived by a polynomial factorization method. The zeroes have broad bandwidths (1.5-2 kHz) and are located periodically with a spacing depending on the effective length. Thus the design of HPC filters for variable effective lengths is trivially achieved. A detailed error analysis for these models is given. The use of the all-zero HPC filters leads to a new type of pole-zero model for vocal tract transmission which can be used either in analog domain or digital domain. Conventionally, for a fixed number of poles and sampling frequency, the length of the vocal tract is assumed to be fixed (i.e. no HPC). However, with the proposed pole-zero model, HPC for variable effective lengths is automatically ensured.