Residual speech signals

The source signal, ealled the residual, can be found by inverse filtering the speech signal with the linear prediction coefficients. 

One of the more challenging unsolved problems is the representation of transient events, such as attacks in musical percussive sounds and plosives in speech, which are neither quasi-periodic nor random. The residual which results from the deterministic/stochastic model generally contains everything which is not deterministic, i.e., everything that is not sine-wave-like. Treating this residual as stochastic when it contains transient events, however, can alter the timbre of the sound, as for example in time-scale expansion. A possible approach to improve the quality of such transformed sounds is to introduce a second layer of decomposition where transient events are separated and transformed with appropriate phase coherence as developed in section 4.4. One recent method performs a wavelet analysis on the residual to estimate and remove transients in the signal [Hamdy et al., 1996] the remainder is a broadband noise-like component. 

If we apply the inverse filtering technique to each frame in the entire speech waveform, we create a sequence of residual signals, one for each frame. A single residual waveform for the whole utterance can be made from these residual fi ames but as the details of this are somewhat subtle, a description of this is left until section 12.6.5. 

In many cases, especially in female or other high pitched speech, the length of the closed phase can be very small, perhaps only 20 or 30 samples. In the autocorrelation method, the initial samples of the residual are dominated by the errors caused by calculating the residual from the zero signal before the window. The high (and erratic) error in the residual can be seen in the first few samples of the residual in Figure 12.17b. For short analysis windows this can lead to a residual dominated by these terms, and for this reason, covariance analysis is most commonly adopted for closed phase analysis. 

Hirai, T., Tenpaku, a., and Shikano, K. Manipulating speech pitch periods according to optimal insertion/deletion position in residual signal for intonation control in speech synthesis. In Proceedings of the International Conference on Speech and Language Processing 2000 (2000). 

Kain, a., and Macon, M. Design and evaluation of a voice conversion algoritiim based on spectral envelope mapping and residual prediction. In Proceedings of the International Conference on Acoustics Speech and Signal Processing 2001 (2001). 

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