Showing papers on "Spectral density estimation published in 1979"

Transient and convergent behavior of the adaptive line enhancer

Abstract: The adaptive line enhancer (ALE) was first described as a practical technique for separating the periodic from the broad-band components of an input signal and for detecting the presence of a sinusoid in white noise. Subsequent work has shown that this adaptive filtering structure is applicable to spectral estimation, predictive deconvolution, speech processing, interference rejection, and other applications which have historically used matrix inversion or Levinson's algorithm techniques. This paper uses an eigenvalue-eigenvector analysis of the expected ALE impulse response vector to demonstrate properties of the convergent filter and to quantify the convergence time and characteristics of the ALE. In particular the ALE's response to a sinusoid plus white noise input is derived and compared to a computer simulation of the ALE with such an input. The eigenvalue-eigenvector technique is then used to evaluate the ALE's performance as an adaptive prewhitener for autoregressive (AR) models with white observation noise. A method is demonstrated which prevents the problem of spectral estimation bias which usually accrues from the observation noise.

Frequency domain coding of speech

Abstract: Frequency domain techniques for speech coding have recently received considerable attention. The basic concept of these methods is to divide the speech into frequency components by a filter bank (sub-band coding), or by a suitable transform (transform coding), and then encode them using adaptive PCM. Three basic factors are involved in the design of these coders: 1) the type of the filter bank or transform, 2) the choice of bit allocation and noise shaping properties involved in bit allocation, and 3) the control of the step-size of the encoders. This paper reviews the basic aspects of the design of these three factors for sub-band and transform coders. Concepts of short-time analysis/synthesis are first discussed and used to establish a basic theoretical framework. It is then shown how practical realizations of subband and transform coding are interpreted within this framework. Principles of spectral estimation and models of speech production and perception are then discussed and used to illustrate how the "side information" can be most efficiently represented and utilized in the design of the coder (particularly the adaptive transform coder) to control the dynamic bit allocation and quantizer step-sizes. Recent developments and examples of the "vocoder-driven" adaptive transform coder for low bit-rate applications are then presented.

The effects of noise on the autoregressive spectral estimator

Abstract: The autoregressive power spectral density estimator possesses excellent resolution properties. However, it has been shown that for the case of a sinusoidal autoregressive process the addition of noise to the time series results in a decrease in spectral resolution. It is proven that, in general, the effect of white noise on the autoregressive spectral estimate is to produce a smoothed spectrum. This smoothing is a result of the introduction of spectral zeros due to the noise. Finally, the use of a large-order autoregressive model to combat the effects of noise is discussed.

Maximum-likelihood spectral estimation

Abstract: A description has been given of some signal processing methods in large array seismology. The optimum detector for a known signal in additive Gaussian noise was shown to consist of the tandem combination of appropriate time delays, maximum-likelihood filter, noise whitening filter, matched filter, and a threshold comparator. The maximum-likelihood filter plays an important role in determining the structure of the optimum detector. This filter also provides a minimum-variance unbiased estimate for the input signal when it is not known, which is the same as the maximum-likelihood estimate of the signal if we have Gaussian noise.

Frequency and bearing estimation by two-dimensional linear prediction

Abstract: Simultaneous frequency and bearing estimation using 2-D spectral analysis of the space-time data array is investigated. The spectral estimates are generated using 2-D linear prediction. It is shown that single-quadrant prediction can lead to severe asymmetry and bias in the estimated spectra; while a certain combination of the results for two adjacent quadrants yields well-behaved spectral estimates.

Nonlinear methods of spectral analysis

Abstract: Prediction-error filtering and maximum-entropy spectral estimation.- Autoregressive and mixed autoregressive-moving average models and spectra.- Iterative least-squares procedure for ARMA spectral estimation.- Maximum-likelihood spectral estimation.- Application of the maximum-likelihood method and the maximum-entropy method to array processing.- Recent advances in spectral estimation.

High resolution spectral estimation for noisy signals

Abstract: A spectral model containing poles and zeros is derived for the high resolution spectral estimation of data containing an auto-regressive (all-pole) signal, interference, and white noise A computationally efficient method for computing the spectrum is introduced Examples of some spectra calculated by this method are presented and compared with the autoregressive spectral estimator

Sources of and remedies for spectral line splitting in autoregressive spectrum analysis

Abstract: Spectral line splitting in autoregressive spectral estimation changes what should be a single spectral line into two or more displaced spectral lines. Fougere was the first researcher to note the existence of certain conditions for sinusoidal data for which splitting occurred. He proposed a complicated gradient-descent algorithm which seems to fix the problem for at least one sinusoid. It is shown that spectral line splitting is a result of estimation errors and is not inherent in the autoregressive approach. In particular, the interaction between positive and negative sinusoidal frequency components in the Burg reflection coefficient and Yule-Walker auto-correlation estimates and the use of the biased autocorrelation estimator in the Yule-Walker approach is responsible for spectral line splitting. Spectral line splitting may be alleviated for one sinusoid by using complex data and also, the unbiased autocorrelation estimator in the Yule-Walker case. Spectral line splitting for multiple sinusoids is discussed.

Adaptive Clutter Filtering Using Autogressive Spectral Estimation

Abstract: A new adaptive filter to reject clutter is derived using autoregressive spectral analysis techniques. The adaptive filter performs open. Ioop processing, resulting in a shorter transient response, and is therefore suitable for radar waveforms containing only a small number of samples. A number of examples including application to ballistic missile defense are presented to demonstrate the performance capabilities of the new adaptive filter.

Spectral line analysis by Pisarenko and Prony methods

Abstract: A comparison of the Pisarenko and Prony approaches to spectral line analysis (sinusoid frequency and power estimation) is presented in this paper. The Pisarenko technique utilizes a statistical approach via the autocorrelation function. The Prony technique utilizes a deterministic approach via a least squares estimation procedure. The Prony method appears to have the edge on the Pisarenko technique. For one, the Prony method has fewer spurious components than does a Pisarenko line analysis. Also, a recursive procedure with lower computational complexity and a means to determine model order (number of sinusoidal components) is available with the Prony approach, a distinct advantage over the Pisarenko method.

Angular Spectra in Radar Applications

Abstract: Recent advances in the art of estimating spectral densities have led to speculation that these same techniques could be used to improve angular resolution in radar applications. An improvement in angular resulution would be particularly helpful in sepingrating low angle returns from their surface reflected images. Despite the duality between time and space, however, it turns out that the low angle radar problem is different from the usual spectral estimation problem in a rather fundamental way. The unfortunate result is that the improved spectral estimation techniques are of little, if any, value in solving the low angle tracking problems.

High-resolution two-dimensional spectral analysis

Abstract: Until recently most high-resolution autoregressive spectral analysis techniques have been applied to analysis of either single-channel waveforms or multichannel vector processes. However, the use of data prediction autoregressive spectral analysis permits the application of some high-resolution single-channel methods to high-resolution spectral analysis of data fields in two or more dimensions. The technique consists of extrapolating observed data beyond the observation window by means of an autoregressive data-generation model. High-resolution spectral analyses are then obtained by conventional discrete Fourier transforms (DFTs) of the extrapolated data.

Fourier transform differences and averaged similarities in diatoms

Abstract: Phase contrast photographs of diatoms are characterized from their Fourier transform taken through an optical diffractometer. The system output is placed on line to a PDP11/40 providing digital subtraction of two output spectral distributions due to different species. Differences obtained in this manner are used for characterizing various species. An average Fourier transform taken through coherent additions is also analyzed to find common features in a given set of diatoms.

Short-time Fourier analysis tecniques for FIR system identification and power spectrum estimation

Abstract: A wide variety of methods have been proposed for system modeling and identification. To date, the most successful of these methods have been time domain procedures such as least squares analysis, or linear prediction (ARMA models). Although spectral techniques have been proposed for spectral estimation and system identification, the resulting spectral and system estimates have always been strongly affected by the analysis window (biased estimates), thereby reducing the potential applications of this class of techniques. In this paper we propose a novel short-time Fourier transform analysis technique in which the influences of the window on a spectral estimate can essentially be removed entirely (an unbiased estimator) by linearly combining biased estimates. As a result, section (FFT) lengths for analysis can be made as small as possible, thereby increasing the speed of the algorithm without sacrificing accuracy. The proposed algorithm has the important property that as the number of samples used in the estimate increases, the solution quickly approaches the least squares (theoretically optimum) solution. The method also uses a fixed Fourier transform length independent of the amount of data being analyzed, allowing the estimate to be recursively updated as more data is made available. The method assumes that the system is a finite impulse response (FIR) system.

Fourier transform method for calculating the transmittance of inhomogeneous atmospheres.

Abstract: For spectral lines with combined Doppler and pressure broadening, the Fourier transform of the line shape is calculated analytically in an isothermal layer in which both the pressure and absorber concentrations vary along the line of sight. Use of the Cooley-Tukey fast Fourier transform algorithm allows efficient computation of the optical depth of such layers containing a large number of absorption lines of the same shape. The computation time is almost independent of the number of absorption lines. In many cases, this method allows increased speed and accuracy compared with conventional line-by-line methods.

Comments on "Frequency estimation by linear prediction "

Abstract: It is shown that contrary to the claims made in the above paper, the analytic signal frequency estimate can be severely biased. The bias manifests itself for short data records and low signal-to-noise ratios.

Circuit for the adaptive suppression of narrow band interference

Abstract: Adaptive suppression of narrow band interference is realized by a filter that automatically makes estimates of interfering signals in the frequency domain and separates the interference from the desired signal. Received analog signals are Fourier transformed in accordance with a CHIRP Z algorithm, squared, and filtered by an N point serial structural CCD to provide a smoothed power spectral density signal. The smoothed power spectral density signal is utilized to cancel interfering signals by any one of three mechanizations. One mechanization comprehends a threshold circuit that generates binary signals in response to the CCD output. The binary signals control a gate that gates strong frequency components (the estimates of the interfering frequency coefficient) from the Fourier transformer through to an inverse Fourier transformer. The inverse Fourier transformed strong frequency components are then subtracted from the delayed received analog signal. A second mechanization transmits the full Fourier transformed spectrum to the inverse Fourier transformer and utilizes the gate to notch out the strong frequency components in response to the CCD output. The third mechanization weights the Fourier transformed frequency coefficients with the smoothed power spectral density signal, inverse transforms the weighted spectrum and subtracts it from the delayed analog signal.

Fast Fourier transform spectral analysis system employing adaptive window

Abstract: A spectral analysis system includes a Fast Fourier Transform (FFT) processor which receives a time domain signal and provides a specified number of initial signal strength estimates, each of the initial estimates being equal to one of the frequency domain coefficients of the Fast Fourier Transform of the time domain signal which is generated when the time domain signal is sampled at a number of intervals equal to the number of initial estimates, over a time period of specified duration. The system further includes an adjustable window element receiving a selected number of the initial estimates for sensing or detecting the presence of a leakage component in a given one of the initial estimates, and for providing an adjusted signal strength estime, the adjusted signal strength estimate comprising the difference between the given initial estimate and the leakage component. A spectral recorder receiving a number of adjusted estimates is provided to record the spectral lines, or frequency components, of the time domain signal, and the relative strengths thereof.

Spectral estimation: An impossibility?

Abstract: Many methods of estimating the power spectrum are based upon the autocorrelation function. As the data is finite in duration, only a portion of the autocorrelation function can be directly estimated. An example of the insufficiency of using only a portion of the autocorrelation function for spectral estimation is discussed.

A separable 2-D autoregressive spectral estimation algorithm

Abstract: In this paper, a direct-data, 2-D spectral estimation technique is presented, in which the 1-D autoregressive properties of the data are exploited independently in both dimensions. For 2-D, multiple complex sinusoids in white noise, a significant improvement in 2-D resolution is obtained.

Microprocessor-based walsh-fourier spectral analyzer

Abstract: A microprocessor-based Walsh-Fourier spectral analyzer is described. It includes the sampling of the incoming signal at 64 times the input signal frequency, using a special purpose frequency multiplier module (FMM), storing the digital data in a permuted sequence in the system memory under the control of a direct memory access (DMA) controller, and performing a fast Walsh-Hadamard transform (FWHT) of the permuted data sequence. The system uses a single board computer SBC80/10 in an Intel System 80/10 and a special purpose board which includes FMM, DMA, and A/D conversion circuits. Fourier coefficients are obtained via a Walsh to Fourier conversion algorithm; the total process is then faster than the Cooley-Tukey FFT algorithm for a data length of 64 or less.

Unbiased spectral estimation and system identification using short-time spectral analysis methods

Abstract: The methods of system identification and spectral analysis are well documented in the literature. In this paper, we attempt to merge the methods of least-square system identification and short-time Fourier transform spectral estimation. Starting from the least-squares normal equations for a linear system identification problem and expanding the signals in short-time Fourier transforms, we derive a Toeplitz system of equations, the solution of which approximates the original least-squares equation solution. We then bound the error norm between the two solution methods and show the properties of the error by numerical methods. The resulting “spectral” estimation method is shown to completely remove the bias normally associated with previously proposed spectral estimation procedures. The method appears to be particularly useful when one is interested in linear system identification of very large systems (long impulses response) or for system identification in the presence of nonstationary (eg., hurst) noise. Extensive numerical results are included.

Method for measuring the spectral distribution of electromagnetic radiation intensity and spectrometer of millimetric and far-infrared ranges for effecting same

Abstract: A method for measuring the spectral distribution of electromagnetic radiation intensity, wherein the spectral distribution of electromagnetic radiation intensity is converted to an electric signal by means of a direct integral Hilbert transform in superconducting weak links. The electric signal as a function of a direct integral Hilbert transform parameter is measured, and the desired spectral distribution of electromagnetic radiation intensity is determined by applying an inverse integral Hilbert transform to the measured function. A spectrometer of millimeter and far-infrared ranges for effecting the above method is provided for determining the frequency spectrum of microwave or infrared radiation signals. The radiation to be measured is modulated, with the modulated signal coupled to a receiver to which a variable scanning voltage is applied by a control unit, the value of the scanning voltage being proportional to a Hilbert transform parameter. The output of the receiver is coupled to a phase detector, to which a reference signal is applied from the modulator; the output of the phase detector is a direct Hilbert transform of the spectral distribution of the input signal (when the Hilbert transform parameter-representing voltage applied to the receiver is scanned through the entire frequency range of the input signal). The spectral distribution is then obtained by deriving the inverse integral Hilbert transform of the output of the phase detector.

An Iterative, Parametric Spectral Estimation Technique for High-Resolution Pulse-Echo Ultrasound

Abstract: Measurement of the slope of attenuation as a function of frequency to compute ultrasonic attenuation coefficients for thin slices of tissue with ultrasonic pulse-echo techniques is fraught with difficulties. Maximum amplitude measurements of the echo's temporal record are subject to error from interference effects as well as nonsteady-state measurement problems. Power spectrums computed from selected time segments invariably include the effect of more than one echo wavetrain, and thus the effect of more than one tissue segment.

Rapid method of forming spectra from regularly sampled records by rectangular wave transforms

Abstract: Spectral estimation of signals sampled at equispaced time instants is discussed. Stable periodogram estimates are generally formed from the squares of Fourier coefficients summed over a large number of data blocks. An exact relationship has been shown to exist between Fourier coefficients and ‘rectangular wave’ transforms, which are obtained when the sinusoidal function is replaced by the associated sign function. The coefficients so formed can be unscrambled into Fourier coefficients. A related operation can also be carried out on the powers formed from the accumulated squared-up estimates, but in this case the deconvolution is not exact. Nevertheless, in many practical situations the method provides a very good approximation to the power spectrum. The approach has the advantage that the rectangular wave coefficients can be generated only by additive operations, and these are much faster to implement on a small microprocessor. The technique is applied to digitally simulated data.

Speech signal processing circuit

Abstract: To improve the speech quality at lower bit rates within a digital communication system in which the coefficients of a frequency transform (e.g. discrete cosine transform) are adaptively encoded with adaptive quantization and adaptive bit-assignment, the adaptation is controlled by a short-term spectral estimate signal formed by combining the formant spectrum and the pitch excitation spectrum of the coefficient signals.

A parameter estimation approach to time delay estimation

Abstract: Present techniques that estimate the difference in arrival time between two signals, corrupted by noise, received at two separate sensors, are based on the determination of the peak of the generalized cross-correlation between the signals. To achieve good resolution and stability in the estimates, the input sequences are first weighted. Invariably, the weights are dependent on input spectra which are generally unknown and hence have to be estimated. By approximating the time shift as a finite impulse response filter, estimation of time delay becomes one of determination of the filter coefficients. With this formulation, a host of techniques in the well developed area of parameter estimation is available to the time delay estimation problem. In addition, the parameter estimation approach is expected to have a smaller variance since it avoids the need for spectral estimation. Indeed, experimental results from two examples show that the time delay estimate, found by least squares parameter estimation, has a smaller variance than the approximate maximum likelihood estimator of Hannan-Thomson where spectral estimation is required.

Constant-Q analysis using the chirp z-transform

Abstract: Constant-Q spectral analysis can be performed by taking the Fourier transform of a windowed sequence where the window is a function of the product of time and frequency If the window used is a decaying exponential whose argument is a constant times the product of time and frequency, the result is equivalent to evaluating the z-transform of the sequence along an outwardly going spiral in the complex z-plane This analysis can thus be implemented using the chirp z-transform algorithm, and is discussed for the specific case of loudspeaker impulse-response measurements