Pole Zero Speech Models Speech is nonstationary. It can approximately be considered stationary over short intervals (20-40 ms). Over thisinterval the source can also be assumed to be stationary (steady pitch, glottal flow or stationary noise source)  Sliding window techniques. Window has to be short enough for “time resolution” and long enough for “frequency resolution”.

All Pole Modelling of Deterministic Signals Linear prediction analysis express a signal in terms of its past samples Let S(z) be the z-transform of speech and U g (z) be the z-transform of vocal-tract input. İn time domain (autoregressive model; AR) A k are linear prediction coefficients. Because H(z) includes glottal flow u g [n] can be considered as an impulse train. It is nonzero only once in a pitch period. One cycle of glottal flow

All Pole Modelling of Deterministic Signals In the context of linear prediction represents a linear predictor of order p. is the predcion of s[n] The predictor is FIR filter of length p. ( ) Prediction error sequence is Prediction error filter is Fig 5.1

All Pole Modelling of Deterministic Signals If S[n] is the output of an AR system and if coefficients  k are the same as a k then the prediction error is the input.