Lossy pole-zero modeling for speech signals

This paper presents an acoustic model-based lossy pole-zero modeling for speech signals, which overcomes the limitation in the existing lossless pole-zero model that forced the numerator part of the pole-zero transfer function to be symmetric. We derive the lossy pole-zero model and its transfer function by employing the wave digital filter (WDF) adaptor formulas and by converting the fixed termination value -1 to a loss factor /spl mu//sub 0//sup c//spl isin/(-1, 1). Then we discuss how to determine the reflection coefficients of the lossy pole-zero model. For this we first employ a well-performing ARMA modeling algorithm for a pole-zero type estimation of the given speech signal and then fit the transfer function of the lossy pole-zero model to that of the ARMA model under Euclidean cost function. This procedure is demonstrated by an example using the Steiglitz-McBride ARMA estimation method with a synthetic speech signal. The lossy pole-zero modeling yields a new filter structure-namely, three-branch lattice structure-which consists of three lattice branches with the third branch terminated by the loss factor /spl mu//sub 0//sup c//spl isin/[-1, 1] and with the three branches connected by a three-port wave adaptor characterized by the area ratio /spl sigma//spl isin/ [0,1]. The three-branch lattice structure is a general filter structure which becomes the lossless pole-zero structure when /spl mu//sub 0//sup c/=-1 and becomes the existing all-pole lattice structure when /spl sigma/=0.