Showing papers by "Patrick J. Loughlin published in 1999"

When is instantaneous frequency the average frequency at each time

Abstract: The interpretation of instantaneous frequency has been a subject of interest for many years. One interpretation is that it is the average frequency at each time in the signal. We prove that instantaneous frequency equals the average frequency at each time only when there is symmetry in the instantaneous spectrum, as previous empirical evidence has suggested. Also, when there is such symmetry, the average frequency at each time equals the median frequency at each time.

Spectrographic measurement of instantaneous frequency and the time-dependent weighted average instantaneous frequency

Abstract: Instantaneous frequency (IF) is an important signal characteristic arising in many fields. It is a concept intimately linked to time–frequency analysis, where it can be obtained from a time–frequency distribution (TFD) as the first conditional moment in frequency, suggesting that the IF is the average frequency at each time. However, this interpretation is questionable, since it is well known that the IF often ranges beyond the spectral support of the signal. In addition, to obtain the IF from a spectrogram (which is one possible TFD), a very wideband—and thus severely spectrally distorted—spectrogram must be used. More reasonable bandwidths are investigated, and, in particular, give the conditions by which the first conditional moment of a spectrogram can indeed be interpreted as the average frequency at each time. Under these conditions, namely when the spectrogram bandwidth is less than the frequency separation of the signal components in the time–frequency plane, the spectrogram yields not the usual IF, but a time-dependent weighted average instantaneous frequency (WAIF) of the signal. Also, while the IF and WAIF are generally different, sometimes they are the same (in particular, when there is symmetry in the time–frequency spectrum of the signal); in that case, the first conditional spectral moments of both wideband and narrow band spectrograms are the same and interpretable as the average frequency at each time.

Denoising using time-frequency and image processing methods

Abstract: We present a number of methods that use image and signal processing techniques for removal of noise from a signal. The basic idea is to first construct a time-frequency density of the noisy signal. The time-frequency density, which is a function of two variables, can then be treated as an 'image,' thereby enabling use of image processing methods to remove noise and enhance the image. Having obtained an enhanced time-frequency density, one then reconstructs the signal. Various time frequency-densities are used and also a number of image processing methods are investigated. Examples of human speech and whale sounds are given. In addition, new methods are presented for estimation of signal parameters from the time- frequency density.

Weighted least-squares implementation of Cohen-Posch time-frequency distributions with specified conditional and joint moment constraints

Abstract: A positivity constrained iterative weighted least-squares (WLS) method for constructing non-negative joint time-frequency distributions (i.e., Cohen-Posch (1985) TFDs) satisfying marginal, joint moment, conditional moment, and generalized marginal constraints, is developed. The new algorithm solves the "leakage" problem of the least-squares approach and is computationally faster. It is also more computationally efficient than the MCE implementation of these constraints developed by Loughlin, Pitton, and Atlas (1994).

Instantaneous bandwidth of multicomponent signals

Abstract: As with the case of instantaneous frequency, it is often difficult to interpret the instantaneous bandwidth of most signals: both quantities typically range beyond the spectral support of the signal, yielding the paradox that the instantaneous bandwidth (and frequency) can be greater than the global bandwidth of the signal. A new definition of instantaneous frequency that does not suffer from this difficulty has recently been given, and we build on those results here to obtain a new definition of instantaneous bandwidth. Kernel constraints for a Cohen-class time-frequency distribution to yield these new results for its conditional moments are also given.

A new multi-window time-frequency approach yielding accurate low-order conditional moments

Abstract: The authors build on Cohen's work on instantaneous bandwidth and frequency by extending it to a multi-window framework. Unlike the case with a single spectrogram, the multi-window framework allows one to obtain a time-varying spectral estimate that simultaneously satisfies instantaneous bandwidth and frequency constraints.

Time‐varying coherent AM–FM demodulation and denoising of acoustic signals

Abstract: Noise removal via linear time‐invariant (LTI) filtering is most effective when the signal and noise spectra have minimal overlap in frequency. In particular, it can be difficult to extract, via LTI filtering, broadband signals from broadband noise, because often their spectra overlap. However, many broadband signals are locally narrow band (e.g., AM–FM signals with large FM and moderate to small AM), and this characteristic can be exploited to improve noise suppression for such signals. We present a method for extracting locally narrow band signals from broadband noise, based on an AM–FM decomposition of the signal and time‐varying filtering. The center frequency and passband of a linear time‐varying filter are determined from estimates of the instantaneous frequency and instantaneous bandwidth of the signal. Results on both synthetic signals and recorded whale sounds in ambient noise demonstrate a significant improvement in SNR compared to LTI‐based filtering. [Supported by ONR Grant N00014‐98‐1‐0680.]

Application of time-frequency methods to sound-quality analysis in automobiles

Abstract: We apply time-frequency methods to automotive vibration signals for sound quality analysis. Our analysis indicates that time-frequency methods provide additional information beyond that provided by the spectral density and vibration time series that is relevant to the assessment of noise and sound quality.

Time-frequency analysis of automobile road data

Abstract: Road vibration tests and road simulation on a shaker table are basic methods used to design and test automobile vehicle components. We show that time-frequency methods can be profitably used to analyze data obtained from actual and simulated road tests. In particular, we discuss how time-frequency methods can be used to interpret the data and to ascertain how accurately the simulated shaker table output is reproducing the actual measured road data.

Time‐frequency analysis: A tutorial review

Abstract: Many signals, such as speech and other animal sounds, FM radio waves, machine vibrations, and sonar and radar echoes, exhibit frequency characteristics that change over time. Standard spectral analysis of such signals provides an incomplete description of the process, because the spectral density reveals only what frequencies existed in the signal, but not when they occurred. Time‐frequency analysis, however, shows how the frequencies change over time and hence is a more complete characterization of these signals. This approach to time‐varying spectral analysis has become standard and has revealed new physical properties of signals. Perhaps the most common method of time‐frequency analysis is the spectrogram, developed over 50 years ago. Many other methods have since been developed, driven largely by a desire to overcome limitations of the spectrogram. Most of these methods were developed by effective use of Cohen’s 1966 formulation for generating time‐frequency distributions (TFDs). A review of the spectrogram and these TFDs, including the Wigner, Choi–Williams, and Zhao–Atlas–Marks distributions, among others, is presented. A variety of applications are shown that illustrate the basic ideas and the different methods. [Work supported by ONR grant N00014‐98‐1‐0680.]

Postural sway response to chirp moving scene perturbations

Abstract: Moving visual scenes with sinusoidal motion have been used to study the role of vision in human balance. We applied a "chirping" visual perturbation (increasing/decreasing frequency of motion), and time-frequency analyzed the resulting center-of-pressure (COP) under the feet in healthy and vestibularly impaired subjects. Differences between healthy and impaired subjects were observed.