Orthogonal Parameters Research Articles

Orthogonal coding of linear prediction log area ratios

In this experimental study, the principal‐components statistical analysis procedure was used to obtain an uncorrelated orthogonal parameter set derived from a linear transformation of LPC log area ratios. The log area ratios of continuous speech for several adult male and female speakers were computed using an autocorrelation linear predictive vocoder analyzer. Group‐averaged principal‐components basis vectors, the coefficients for the linear transformations of the log area ratios, were calculated for the male and female speaker groups. Speech was synthesized with a residual‐excited LP vocoder using LP coefficients derived from a small number of group‐averaged log area ratio principal‐components factors. A sentence preference experiment was conducted in order to compare speech synthesized from LP log area ratio principal components versus speech synthesized from spectral band energy principal components and speech synthesized from a standard LP vocoder. The results of the sentence preference experiment indicate that the orthogonal LP log area ratio parameters are inferior to both spectral band‐energy orthogonal parameters and to the original LP coefficients, in terms of the information retained for a given number of parameters. The apparent discrepancy in the findings of the present study versus the results of an earlier experiment [M. R. Sambur, “An Efficient Linear Prediction Vocoder,” Bell Syst. Tech. J. 54, 1693–1723 (1975)] is probably due to the analysis techniques of the previous experiment (analysis applied separately for each sentence and each speaker) as compared to the more general analysis conditions of the present study (one set of basis vectors used to characterize a long speech passage for several speakers).

Quantification of the Frank and McFee-Parungao orthogonal electrocardiogram in valvular pulmonic stenosis. Correlations with hemodynamic measurement

In 66 patients with congenital valvular pulmonic stenosis and intact ventricular septum, correlations were obtined among various multiple hemodynamic and orthogonal vectorcardiographic parameters. The Frank and McFee-parungao lead systems were used. The most important hemodynamic parameter evaluated was right ventricular pressure (RVP). RVP correlated best with X terminal to the right (XTR) in both Frank (R = 0.68) and McFee (R = 0.61) systems. The correlation between RVP and Z anterior was poor. The direction of the initial QRS vector on the X axis was helpful in predicting severity. With X initial to the right, especially in McFee, the RVP is most likely to be systemic or less, while with X initial to the left, the RVP is frequently but not necessarily suprasystemic. T vector spatial orientation is not helpful in the assessment of severity.

Speaker recognition using orthogonal linear prediction

Recent experiments in speech synthesis have shown that, by an appropriate eigenvector analysis, a set of orthogonal parameters can be obtained that is essentially independent of all linguistic information across an analyzed utterance, but highly indicative of the identity of the speaker. The orthogonal parameters are formed by a linear transformation of the linear prediction parameters, and can achieve their recognition potential without the need of any time-normalization procedure. The speaker discrimination potential of the linear prediction orthogonal parameters was formally tested in both a speaker identification and a speaker verification experiment. The speech data for these experiments consisted of six repetitions of the same sentence spoken by 21 male speakers on six separate occasions. For both identification and verification, the recognition accuracy of the orthogonal parameters exceeded 99 percent for high-quality speech inputs. For telephone inputs, the accuracy exceeded 96 percent. In a separate text-independent speaker identification experiment, an accuracy of 94 percent was achieved for high-quality speech inputs.

Speaker recognition using orthogonal linear prediction

The effectiveness of a set of speaker recognition features is usually characterized in terms of the ratio of the interspeaker variability of the feature to its intraspeaker variability (F-ratio). A recent experiment in speech synthesis [M.R. Sambur, “An Efficient LPC Vocoder,” Bell Syst. Tech. J. (to be published)] has shown that by an appropriate eigenvector analysis, a set of orthogonal parameters can be obtained that is essentially constant across an utterance for a given speaker (i.e., zero intraspeaker variability). If the same eigenvector analysis is applied to the same utterance spoken by another speaker, the resulting values of the orthogonal parameters are, however, different. These orthogonal parameters were therefore examined for their ability to differentiate different speakers. They were formally tested in a speaker recognition experiment involving 21 speakers. The speech data consisted of six repetitions of the same sentence spoken by each speaker on six separate occasions. The identification and verification accuracy of the orthogonal parameters exceeded 99%.

Day to day variation in 3 orthogonal lead electrocardiogram parameters after acute myocardial infarction.

Day to day variation in 3 orthogonal lead electrocardiogram parameters after acute myocardial infarction.

A Bracketing Rule for the Estimation of Simple Distributed Lag Models

T HE geometric distributed lag model developed by Koyck [8] and Nerlove [11] has been widely used in many empirical studies. The appropriate estimation method for parameters of these models is determined by the true probability distribution of random errors. If the random errors follow a first-order Markov process, Klein [7] has shown that the method of weighted regressions yields maximum likelihood estimators.' However, Klein's method requires prior knowledge of the true serial correlation of random errors. In the absence of such prior knowledge, one can resort to several alternative estimation methods.2 In this paper, I establish a bracketing rule applicable to a subset of the admissible probability distributions of random errors. Consider two special cases of Klein's method in which the true serial correlation p is (i) equal to zero and (ii) equal to the coefficient of the lagged dependent variable (1 X). The former case implies an orthogonal regression while the latter is equivalent to ordinary least squares (OLS). The orthogonal and OLS regressions yield two sets of parameter estimates lying on either side of the maximum likelihood parameter estimates provided that the true serial correlation lies in the interval 0 < p < 1 L, the OLS estimate of the population parameter 1 X. This basic bracketing theorem can be shown to hold even for fixed sample size. Moreover, the width of the interval bracketing the maximum likelihood parameter estimates is narrower, the larger is the partial correlation with the lagged dependent variable. This last result leads to an important implication. If a geometric distributed lag constitutes the correct specification of economic behavior, the dependent variable should be highly correlated with the lagged dependent variable. In this event, the discrepancy between OLS and orthogonal parameter estimates (which bracket the maximum likelihood estimates) will be small. Thus, the bias due to least squares is negligibly small provided that the true serial correlation lies in the interval 0 < p < 1 X. A simple geometric distributed lag model is described by a system of two structural equations. Yt a + 8Zt* + Ut + (1)