Frequency domain

About: Frequency domain is a research topic. Over the lifetime, 53871 publications have been published within this topic receiving 701364 citations.

Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media

Abstract: From experimental studies in digital processing of seismic reflection data, geophysicists know that a seismic signal does vary in amplitude, shape, frequency and phase, versus propagation time To enhance the resolution of the seismic reflection method, we must investigate these variations in more detail. We present quantitative results of theoretical studies on propagation of plane waves for normal incidence, through perfectly elastic multilayered media. As wavelet shapes, we use zero-phase cosine wavelets modulated by a Gaussian envelope and the corresponding complex wavelets. A finite set of such wavelets, for an appropriate sampling of the frequency domain, may be taken as the basic wavelets for a Gabor expansion of any signal or trace in a two-dimensional (2-D) domain (time and frequency). We can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals. These results appear as complex 2-D functions of time and frequency, i.e., as “instantaneous frequency spectra. ’ ’ Choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces. For this purpose, we developed a Gabor expansion involving basic wavelets with a constant time duration/mean period ratio. For layered media, as found in sedimentary basins,

Signal processing apparatus and method

Abstract: A method and an apparatus to analyze two measured signals that are modeled as containing desired and undesired portions such as noise, FM and AM modulation. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, a transformation is used to evaluate a ratio of the two measured signals in order to find appropriate coefficients. The measured signals are then fed into a signal scrubber which uses the coefficients to remove the unwanted portions. The signal scrubbing is performed in either the time domain or in the frequency domain. The method and apparatus are particularly advantageous to blood oximetry and pulserate measurements. In another embodiment, an estimate of the pulserate is obtained by applying a set of rules to a spectral transform of the scrubbed signal. In another embodiment, an estimate of the pulserate is obtained by transforming the scrubbed signal from a first spectral domain into a second spectral domain. The pulserate is found by identifying the largest spectral peak in the second spectral domain.

Modal Identification of Output-Only Systems using Frequency Domain Decomposition

Abstract: In this paper a new frequency domain technique is introduced for the modal identification of output-only systems, i.e. in the case where the modal parameters must be estimated without knowing the input exciting the system. By its user friendliness the technique is closely related to the classical approach where the modal parameters are estimated by simple peak picking. However, by introducing a decomposition of the spectral density function matrix, the response spectra can be separated into a set of single degree of freedom systems, each corresponding to an individual mode. By using this decomposition technique close modes can be identified with high accuracy even in the case of strong noise contamination of the signals. Also, the technique clearly indicates harmonic components in the response signals.

Applied system identification

Abstract: 1. Introduction. 2. Time-Domain Models. 3. Frequency-Domain Models. 4. Frequency Response Functions. 5. System Realization. 6. Observer Identification. 7. Frequency Domain System ID. 8. Observer/Controller ID. 9. Recursive Techniques. Appendix A: Fundamental Matrix Algebra. Appendix B: Random Variables and Kalman Filter. Appendix C: Data Acquisition.

Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources

Abstract: This paper presents a method of constructing a single signal subspace for high-resolution estimation of the angles of arrival of multiple wide-band plane waves. The technique relies on an approximately coherent combination of the spatial signal spaces of the temporally narrow-band decomposition of the received signal vector from an array of sensors. The algorithm is presented, and followed by statistical simulation examples. The performance of the technique is contrasted with other suggested methods and statistical bounds in terms of the determination of the correct number of sources (detection), bias, and variance of estimates of the angles.