ch8_lpc

# ch8_lpc - MIT OpenCourseWare http/ocw.mit.edu HST.582J...

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MIT OpenCourseWare http://ocw.mit.edu HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing Spring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Harvard-MIT Division of Health Sciences and Technology HST.582J: Biomedical Signal and Image Processing, Spring 2007 Course Directors: Dr. Julie Greenberg HST582J/6.555J/16.456J Biomedical Signal and Image Processing Spring 2007 Chapter 8 - LINEAR PREDICTION c ± Bertrand Delgutte 1999 Introduction Linear prediction is a widely-used signal processing technique in which the current value of a discrete-time signal is approximated by a ﬁnite weighted sum of its past values. It is mathemat- ically equivalent to the techniques of autoregressive spectral estimation, and maximum-entropy estimation. The central idea behind these techniques is that the signal is modeled as the response of an all-pole (autoregressive) ﬁlter to a white signal. Spectral estimation is then equivalent to estimating the coeﬃcients of the all-pole ﬁlter. These techniques are well suited to signals whose spectra show sharp peaks such as the formants of speech. In the case of speech signals, linear prediction takes a special signiﬁcance in the context of the source-ﬁlter model of speech production. According to this model, speech is the output of a time-varying ﬁlter (representing the vocal tract resonances and radiation characteristics) ex- cited by either a voicing source or a noise source (Fig. 1a). Under certain assumptions, linear prediction can separate the contributions of the source and the ﬁlter to the speech signal, i.e. it can deconvolve the source signal from the impulse response of the ﬁlter. This property con- trasts with those of the short-time Fourier transform, which provides a spectral representation of speech in which e±ects of the source and the ﬁlter are scrambled, and which is heavily dependent on the choice of an analysis window. The deconvolution property of linear prediction is useful in biomedical applications because the source and the ﬁlter correspond to di±erent anatomi- cal structures, and are therefore a±ected by di±erent clinical conditions. Linear prediction is also widely used in telecommunication engineering and automatic speech recognition because it represents speech in terms of a small number of parameters that contain the most important information for intelligibility. 8.1 All-pole model of speech 8.1.1 From the source-±lter model to the all-pole model In order to show how linear prediction can separate the contributions of the source and the ﬁlter to speech, we need to simplify somewhat the speech-production model of Fig. 1a by making two additional assumptions: (1) that the ﬁlter is all-pole (purely-recursive, or autoregressive) and (2) that the source is ”white” in the sense that it has a ﬂat spectral envelope.
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ch8_lpc - MIT OpenCourseWare http/ocw.mit.edu HST.582J...

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