Linear predictive coding

Knudsen, 1975] Knudsen, M. J. (1975). Real-Time Linear-Predictive Coding of Speech on the SPS-41 Triple-Microprocessor Machine. IEEE Trans. Acoustics Speech and Signal Processing, ASSP-23(1) 140-145. 

The scattering equations are illustrated in Figs. 10.6b and 10.7. In linear predictive coding of speech, this structure is known as the Kelly-Lochbaum scattering junction,... 

In prior chapters we found that spectral shape is important to our perception of sounds, such as vowel/consonant distinctions, the different timbres of the vowels eee and ahh, etc. We also discovered that sinusoids are not the only way to look at modeling the spectra of sounds (or soimd components), and that sometimes just capturing the spectral shape is the most important thing in parametric sound modeling. Chapters 5 and 6 both centered on the notion of additive synthesis, where sinusoids and other components are added to form a final wave that exhibits the desired spectral properties. In this chapter we will develop and refine the notion of subtractive synthesis and discuss techniques and tools for calibrating the parameters of subtractive synthesis to real sounds. The main technique we will use is called Linear Predictive Coding (LPC), which will allow us to automatically fit a low-order resonant filter to the spectral shape of a sound. 

Subtractive synthesis uses a complex source wave—such as an impulse, a periodic train of impulses, or white noise—to excite a spectral-shaping filter. Linear prediction, or linear predictive coding (LPC), gives us a mathematical technique for automatically decomposing a sound into a source and a filter. For low order LPC (6-20 poles or so), the filter is fit to the coarse spectral... 

In prior chapters we looked at subtractive synthesis techniques, such as modal synthesis (Chapter 4) and linear predictive coding (Chapter 8). In these methods a complex source is used to excite resonant fQters. The source usually has a flat spectnun, or exhibits a simple roll-off pattern like f or ip (6 dB or 12 dB per octave). The filters, possibly time-varying, shape the spectrum to model the desired sound. 

This turns out to have important implications for many algorithms. For example, linear predictive coding (Chapter 8) minimizes the least-squared error in both the time and frequency domains, because the sum of squares of the time error signal is equal to the sum of squares of the spectral magnitude error. 

Linear predictive coding (LPC) is a typical example of subtractive resynthesis employing predictive analysis. The result of the predictive analysis stage is a series of snapshots, called LPC frames, which contain the information required to resynthesise the sound. This information may vary in different implementations of the LPC algorithm, but it generally includes the following ... 

CCITTrecG728, 1992] CCITTrecG728 (1992). Coding of speech at 16 kbit/s using low-delay code excited linear prediction. ITU-T. Recommendation G.728. 

Linear prediction was in fact primarily developed for use in speech coding applications. As we have just seen, performing LP analysis allows us to deconvolve the signal into a source and filter, which can then be used to reconstruct the original signal. Simply separating the source and filter... 

Any reduction in potential gain from the use of just four subbands can be compensated for by linear prediction, which aims to remove spectral redundancies remaining in the subbands. With the inclusion of linear prediction, the total performance of the coder can easily match the subband gain associated with the use of many more subbands, without resorting to an increase in filter complexity or coding delay. 

Recently, Gasteiger et al. [59] reported several models to predict human oral bioavailability using Hou and Wang s data set. A set of ADRIANA.Code and Cerius2 descriptors were calculated, and MLR analysis was performed. The best linear model had r2 of 0.18 and RMSD of 31.15. When a set of subsets was cherry-picked so that each subset had either a common functional group or a similar pharmacological activity, the r2 values were improved and RMSD values dropped. But the performance of those models was still not satisfactory the standard errors were above 20.0 and r2 was lower than 0.6. 

Fuchs, 1995] Fuchs, H. (1995). Improving MPEG audio coding by backward adaptive linear stereo prediction. In Proc. of the 99th. AES-Convention. Preprint 4086. 

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