Forward-backward Linear Prediction Method Research Articles

Noise-Reduced Complex LPC Analysis for Formant Estimation of Noisy Speech

In this paper we present a complex linear prediction analysis method for estimating the formant frequencies of noisy speech. The proposed method effectively utilizes the signal (being the analytic signal) which is ignored in the conventional complex linear prediction analysis to achieve noise reduction. Also, the covariance and forward-backward linear prediction (FBLP) methods are compared, and the FBLP method is deployed for predictive coefficients estimation in the proposed method. Experimental results show that the proposed method yields better performance of formant estimation when compared to some conventional methods in white noise. 

An enhanced Fourier transform spectrometer with a search algorithm

Interferometric instruments have the following serious weak points: (1) the necessity of doing a Fourier transform that involves a vast amount of calculation; (2) the lack of knowledge of suitable measuring conditions until the Fourier transform is finished; and (3) the spectral resolution of the conventional Fourier-based techniques is significantly affected by the sampling rate, data length, and noise in signal processing. In this paper, an enhanced spectrometer is proposed using the modified forward-backward linear prediction method (MFBLP) with a search algorithm. To document the advantage of the method presented, a computer simulation for multiple-wavenumber estimation is investigated. The MFBLP method is truly superior to the fast Fourier transform (FFT) method. In general, the spectral resolution using the FFT method is proportional to the data length. In this paper, however, it is shown that excellent results can also be obtained from only 60 sample points using the FFT method. Moreover, from experimental results, we also conclude that the sampling rate must be consistent with the condition 632<f/sub p//spl middot/t/spl middot/D<3164, where f/sub p/, represents the value of the pulse generator frequency in Hz, t the observation time, and D the decimation factor.

Linear estimation of frequencies of multiple sinusoids with least-absolute error criterion

The estimation problem of sine wave frequencies is investigated. The forward-backward linear prediction method (FBLP1) with least-absolute error criterion is used to improve the frequency estimate performance attained by the linear prediction method (FBLP2) with the least-square error criterion. Theoretical and computer simulations show that the FBLP1 method has performances similar and superior to the FBLP2 method.

A Subspace Based Analysis of the Modified Forward-Backward Linear Prediction Method

In recent years, there has been much activity in the application of forward-backward linear prediction (FBLP) method to estimation of frequencies of sinusoids corrupted by white noise. More recently, Tufts and Kumaresan [1] suggested key modifications to the conventional FBLP method. For the modified FBLP method, they have experimentally shown that the prediction order M=3N/4, where N denotes the number of data samples, yields best frequency estimation performance.In this paper, we attempt to develop a subspace-based analysis to explain why the performance of the modified FBLP method is superior for the above value of the predictor order. In this analysis, we use the quality of the signal subspace of the estimated autocorrelation matrix as the performance measure and relate this to the predictor order M. The value of M for which the quality is the highest is referred to as the optimal predictor order, and for N= 25 and 48, the near-optimal predictor order matches with the value 3N/4. Computer simultaions are used to support our assertions.

Performance evaluation of the modified FBLP method for angle of arrival estimation using real radar multipath data

The paper presents the results of a detailed evaluation of the modified forward-backward linear prediction (FBLP) method used for angle of arrival estimation in a low-angle tracking radar environment. The results are based on real radar data pertaining to an angular separation of less than one standard beamwidth between the direct and image components impinging on the radar antenna. The results confirm the superior performance of this method compared to a conventional FFT beamformer. The paper also includes a brief review of the modified FBLP method.

A limitation of the Kumaresan-Prony algorithm in direction-finding applications

A modification of the forward-backward linear prediction method of spectral analysis due to Tufts and Kumaresan was evaluated for use in direction finding with an array of sensors. A special case of this method, called the Kumaresan-Prony case, is especially attractive due to its ease of computation. This case, however, was found to exhibit blind angles, where performance was severely degraded in spite of wide spacing of the sources. The locations of these blind angles are functions of the relative phase of the two sources, and of the ratio of the physical length of the array to the length of the modulation envelope set up by the interference of the two incoming signals.

Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood

The frequency-estimation performance of the forward-backward linear prediction (FBLP) method of Nuttall/Uhych and Clayton, is significantly improved for short data records and low signal-to-noise ratio (SNR) by using information about the rank M of the signal correlation matrix. A source for the improvement is an implied replacement of the usual estimated correlation matrix by a least squares approximation matrix having the lower rank M. A second, related cause for the improvement is an increase in the order of the prediction filter beyond conventional limits. Computationally, the recommended signal processing is the same as for the FBLP method, except that the vector of prediction coefficients is formed from a linear combination of the M principal eigenvectors of the estimated correlation matrix. Alternatively, singular value decomposition can be used in the implementation. In one special case, which we call the Kumaresan-Prony (KP) case, the new prediction coefficients can be calculated in a very simple way. Philosophically, the improvement can be considered to result from a preliminary estimation of the explainable, predictable components of the data, rather than attempting to explain all of the observed data by linear prediction.

Improved spectral resolution

Two new methods are presented for the estimation of the frequencies of closely spaced complex valued sinusoidal signals in the presence of noise. The most effective method is a computationally efficient method for realization of maximum likelihood or maximum posterior probability estimates of the frequencies. The second method is a class of algorithms for removing some of the deficiencies of present adaptive filtering and correlation-estimation approaches to estimation of frequencies, such as the forward-backward linear prediction method. In both of these new methods one is fitting a signal model to data. In method 1 the data are the observed samples of two complex sinusoids plus noise. In the second method the data are elements of an estimated correlation matrix, or of some of its eigenvectors, obtained from the observed samples.