Spectral density estimation

About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.

Fully digital spectrum analyzer using time compression and discrete fourier transform techniques

Abstract: A fully digital spectrum analyzer accepting as an input either an analog signal or a series of digital numbers and using time compression and DFT (Discrete Fourier Transform) techniques to provide the spectral component values of the input signal. Novel techniques and means are used in obtaining the power values for selected spectral lines and in averaging these power values. Statistically controlled noise is added to the input of the spectrum analyzer to enhance its resolutin beyond the resolution which would be otherwise available. Advanced and efficient techniques are used for generating and applying trigonometric functions in the course of finding the real and imaginary part of Fourier transforms, and for providing running averages of the power spectra.

Generalization of the Wiener-Khinchin theorem

Abstract: We generalize the concept of the autocorrelation function and give the generalization of the Wiener-Khinchin theorem. A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set. In addition, we present a partial generalization where the density is the Fourier transform of the characteristic function but the characteristic function is defined in terms of an arbitrary basis set. Both the deterministic and random cases are considered.

Smoothing spline ANOVA for time-dependent spectral analysis

Abstract: In this article we propose a smoothing spline ANOVA model (SS-ANOVA) to estimate and to make inference on the time-varying log-spectrum of a locally stationary process. The time-varying spectrum is assumed to be smooth in both time and frequency. This assumption essentially turns a time-frequency spectral estimation problem into a 2-dimensional surface estimation problem. A smooth localized complex exponential (SLEX) basis is used to calculate the initial periodograms, and a SS-ANOVA is fitted to the log-periodograms. This approach allows the time and frequency domains to be modeled in a unified approach and jointly estimated. Inference procedures, such as confidence intervals, and hypothesis tests proposed for the SS-ANOVA can be adopted for the time-varying spectrum. Because of the smoothness assumption of the underlying spectrum, once we have the estimates on a time-frequency grid, we can calculate the estimate at any given time and frequency. This leads to a high computational efficiency, because for ...

Noise reduction by using spectral decomposition and non-linear transformation

Abstract: A noise reduction system for enhancing noisy speech signals by performing a spectral decomposition on the signal, passing each spectral component through a non-linear stage which progressively attenuates lower intensity spectral components (uncorrelated noise) but passes higher intensity spectral components (correlated speech) relatively unattenuated, and reconstituting the signal. Frames of noisy signal are transformed into the frequency domain by an FFT (Fast-Fourier Transform) device, with windowing. Each transformed frame is then processed to effect a non-linear transfer characteristic, which is linear above a soft "knee" region, and rolls off below, and transformed back to a reconstituted time-domain signal with reduced noise by an IFFT (Inverse Fast Fourier Transform) device (with overlapping). A level control matches the signal to the characteristic. In further embodiments, the characteristic may vary between frequency bands, and may be matched to speech formants by tracking formants using an LSP (Linear Spectral Pairs) technique.