Showing papers on "Spectral density estimation published in 1974"

On the calculation of filter coefficients for maximum entropy spectral analysis

Abstract: The maximum entropy method (MEM) for spectral analysis was suggested by Burg (1967). Its mathematical properties have been discussed in detail by Lacoss (1971), Burg (1972), and Ulrych (1972b) who found that the MEM in general is superior to the more conventional methods of spectral estimation. It has, for example, better resolution and gives more realistic power estimates, especially for short data records. However, the application of the method in the analysis of more complicated geophysical data series is reported in a surprisingly small number of papers. Ulrych (1972a) successfully used the MEM for the analysis of data on long period geomagnetic reversals.

Spectral Estimation of Time Delay for Dispersive and Non‐Dispersive Systems

Abstract: SUMMARY The problem considered is that of measuring the delay between the receipt of a signal at two sites where noise, incoherent between the two sites and with the signal, is also received at each site. In the case where the signal is dispersive the delay will be a function of frequency. The optimum solution involves a proper weighting of the phase shifts at each frequency, the weighting being dependent only on the coherence. The asymptotic distribution of the estimate is given. The method is worked out in detail for various special cases and is illustrated by an oceanographic example. The case where there are more than two sites is briefly discussed. A discussion is also given of the virtues of the method, of some possible variations to it and of some practical considerations.

Identification and autoregressive spectrum estimation

Abstract: In recent years there has been increasing interest in autoregressive spectrum estimation. This procedure fits a finite autoregression to the time series data, and calculates the spectrum from the estimated autoregression coefficients and the one step prediction error variance. For multivariate time series, the estimated autoregressive matrices and one step prediction covariance matrix produce estimates of the spectra, coherences, phases, and group delays. The use of Akaike's information criterion (AIC) for identification of the order of the autoregression to be used makes the procedure objective. Experience gained from analyzing large amounts of data from the biological and physical sciences has indicated that AIC works very well for model identification when compared to more subjective procedures such as the examination of partial F -statistics. This experience has also indicated that using both autoregressive spectrum estimation and classical spectrum estimation and superimposing the plots gives a much stronger feeling for the shape of the true spectrum being estimated. The results of some of these analyses are presented.

Coarse frequency estimation using the discrete Fourier transform (Corresp.)

Abstract: The discrete Fourier transform (DFT) is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise. Probability of anomaly and the variance of the estimation error are determined by computer simulation for several DFT block sizes as a function of signal energy-to-noise density ratio \mathcal{E}/N_0 . Several data windows are considered, but uniform weighting gives the best performance.

Periodic Splines and Spectral Estimation

Abstract: The theory of periodic smoothing splines is presented, with application to the estimation of periodic functions. Several theorems relating the order of the differential operator defining the spline to the saturation (order of bias) of the estimator are proven. The linear operator which maps a function to its periodic continuous smoothing spline approximation is represented as a convolution operator with a given convolution kernel. This operator is shown to be the limit of a sequence of operators which map a function into the periodic version of the usual lattice smoothing spline. The convolution kernel above appears as the kernel in a kernel type estimate of the spectral density. Thus, it is shown that, a smoothing spline spectral density estimate, is also asymptotically a kernel type spectral density estimate. Some numerical results are presented.

Unequal bandwidth spectral analysis using digital frequency warping

Abstract: The application to unequal bandwidth and vernier spectrum analysis of a technique referred to as digital frequency warping is discussed. In this technique a sequence is transformed in such a way that the Fourier transforms of the original and transformed sequences are related by a nonlinear transformation of the frequency axis. An equal bandwidth analysis carried out on the transformed sequence then corresponds to an unequal bandwidth analysis of the original sequence. A comparison is presented between the bandwidth as a function of frequency for the digital warping technique and proportional bandwidth analysis. An analysis of the effects of finite register length in implementing digital frequency warping is also presented.

On the Spectral Density of a Cyclostationary Process

Abstract: A new approach to the spectral-density concept of a cyclostationary process is presented. This approach is based on the observation that a cyclostationary process can be split into a number of wide-sense stationary subprocesses. The spectral densities of these subprocesses, defined as the Fourier transform of their autocorrelation functions, are nonoverlapping functions of frequency. The sum of the spectral densities of these wide-sense stationary subprocesses yields the well-known expression for the spectral density of a cyclostationary process.

Spectral and Short Term Stability Measurements

Abstract: The noise performance of an oscillator can be given either in the spectral or in the time domain. Two types of apparatus are generally necessary to measure these noise characteristics, spectral analyzers and frequency counters. The system described uses spectral density to time domain conversion and measures both the short term frequency stability and the phase spectral density of an oscillator. Bias functions, depending on the spectral density, are calculated. They are used to determine systematic errors introduced by the apparatus.

Spectrum of geomagnetic horizontal intensity in low latitudes in the range 12 to 60 days

Abstract: Low latitude geomagnetic data over a length of 37 years is analysed using fast Fourier transform (FFT). The technique, besides being computationally efficient, permits analysis of long series, so essential for reducing noise level to a degree where weak signals can be detected with statistical reliability and has the added advantage of yielding high resolution power spectrum. In the present communication, spectral estimates are computed in the period range of 12 to 60 days and statistically significant spectral lines, particularly those in the 25–31 day range and those in the vicinity of 13·5 days are discussed.

Asymptotic statistics of periodogram-type spectral estimates for the output of nonlinear devices (Corresp.)

Abstract: The high resolution statistics of a periodogram-type spectral estimate for a periodic deterministic signal plus Gaussian noise are well understood. If, however, the signal plus noise is first passed through a nonlinear memoryless device (such as a hard limiter), the situation becomes much more complicated. The main result of this correspondence is the derivation of the high resolution limit of the joint statistics of the I and Q components of a periodogram for a certain class of nonlinear devices with a deterministic periodic signal and Gaussian noise as input. This result permits the calculation of the asymptotic central moments of the spectral estimate formed from the foregoing periodogram. It then becomes possible to subject a device employing this technique for spectral estimation to a detailed performance analysis.

Some extensions to digital signal processing

Abstract: Some practical extensions to digital signal processing techniques are presented Firstly, an account is given of a curve-fitting procedure designed to give a detailed analysis of time functions, either wholly or in part dominated by a single sinewave, such as an amplitude or frequency-modulated carrier The remainder, and large majority, of the thesis is devoted to the discrete Fourier transform (DFT) and power spectral estimation Two binary transforms, the Walsh and the new Intermediate Binary Transform, are related theoretically to the DFT to give practical computational procedures, which prove to be more flexible than the 'fast' Fourier transform and more efficient for short length data sequences Approximations in the calculations leading to power spectral estimates are proposed and examined In particular, round-off to the nearest integer power of two is applied to the transform coefficients of the DFT procedures An important principle here is the phase invariance property which permits harmonics to be normalised individually, and the errors to be viewed purely in terms of harmonic leakage An isometric plotting routine is used to provide a convenient form of display for functions of three variables, and examples are given of both time-varying power spectra of a single channel electroencephalogram recording and the harmonic leakage due to the said round-off

Noise Reduction by Adaptive Threshold in Digital Signal Processing

Abstract: Wide band digital signal processing systems are becoming increasily important due to the advance of high speed digital Fourier analyzers. This paper presents a new threshold scheme that adaptively reduces noise effect in a data processing system that receives signals corrupted by non-stationary colored noise. The corrupted signal is decomposed into spectral segments by a discrete Fourier transform (DFT) unit and the resulting spectrum is processed by an adaptive threshold unit. The adaptive threshold network is tasked to estimate the noise level and to subtract this noise estimate from the composite signal plus noise to arrive at a high quality signal. For each set of DFT outputs, a finite order polynomial is used to approximate the average noise level by least squares method. The key feature in this polynomial approach is the reduction of the number of parameters characterizing the threshold. The results of this work show that second order can be sufficient, hence comparing to actual number of spectral values (generally greater than 512), the polynomial approach represents a large reduction in computation time and hardware circuit elements. The adaptive algorithm used in this work to estimate the -parameters sequentially is derived from adaptive estimation theory, which has been successfully implemented in a digital signal processing system.

In situ narrow-band calibration of an acoustic receiver

Abstract: A technique for in situ narrow-band calibration of an acoustic receiver is described. Wide-band Gaussian noise is applied through a random acoustic channel to the receiver and a reference. The resultant output spectra are estimated via Welch's method [1], and the unknown amplitude frequency response is estimated from the ratio of the two spectra. Statistical accuracies of the estimates are investigated. For a specified statistical accuracy, the estimate of the unknown amplitude frequency response is found to require the computation of only one-fourth as many discrete Fourier transforms (DFT's) as the estimates of the two power spectra. That is, where N DFT's are necessary to estimate the two power spectra with a specific accuracy, only N/4 DFT's are needed to estimate, with the same accuracy, the ratio of the spectra.