General performance analysis of the shift covariant class of quadratic timefrequency distributions (TFDs) as instantaneous frequency (IF) estimators, for an arbitrary frequency-modulated (FM) signal, is presented. Expressions for the estimation bias and variance are derived. This class of distributions behaves as an unbiased estimator in the case of monocomponent signals with a linear IF. Howev...

We present a method for estimating the instantaneous frequency of a signal. This method involves the calculation of a time–frequency energy density of the signal, then obtaining an instantaneous frequency estimate from this joint density. Time–frequency energy density is calculated as a least squares optimal combination of multi–window Gabor based evolutionary spectra. The optimal weights are o...

This paper gives an overview of existing instantaneous frequency (IF) estimation methods divided into several major categories. One of the first IF estimation approaches was based on the spectrogram, the resolution of which is highly window size dependant. In order to improve the IF estimation accuracy, the iterative method was proposed, such that each iteration gives more accurate estimation o...

It is often claimed that instantaneous frequency, taken as the derivative of the phase of the signal, is appropriate or meaningful only for mono-component signals, and that for multi-component signals a weighted average of individual instantaneous frequencies should be used. In this paper, we show if a signal is decomposed adaptively and we compute the matching pursuit distribution, then the fi...

We consider kernel estimators of the instantaneous frequency of a slowly evolving sinusoid in white noise. The expected estimation error consists of two terms. The systematic bias error grows as the kernel halfwidth increases while the random error decreases. For a nonmodulated signal, g(t), the kernel halfwidth which minimizes the expected error scales as h ∼ [ σ2 N |∂2 t g |2 ]1/5 , where σ2 ...

The Carson and Fry (1937) introduced the concept of variable frequency, required to the theory of frequency modulation (FM), as a generalization of the definition of constant frequency. Moreover, the nonstationary nature of the signals and nonlinear systems require the idea of instantaneous frequency (IF). It is also the basis of the time-frequencyenergy (TFE) analysis of a signal. The IF is th...

The electroencephalogram (EEG), used to noninvasively monitor brain activity, remains the most reliable tool in the diagnosis of neonatal seizures. Due to their nonstationary and multi-component nature, newborn EEG seizures are better represented in the joint time–frequency domain than in either the time domain or the frequency domain. Characterising newborn EEG seizure nonstationarities helps ...

In this paper, our aim is to derive a phase spectrum representation computed via the short-time Fourier transform. Specifically, we are interested in developing a narrow-band speech representation – employing 20-40 ms analysis windows. Furthermore, this representation should be as physically meaningful as the magnitude spectrum. To achieve these ends, we concentrate on instantaneous frequency (...

Estimation of the magnitude and frequency of maximum instantaneous discharges and hydrographs are used for a variety of purposes, such as the design of bridges, culverts, flood-control structures; and the management and regulation of floodplains. Fuller (1914), developed a flood-frequency formula based on analysis of flood peaks in hundred of streams to provide simple methods of estimating maxi...

estimation of the magnitude and frequency of maximum instantaneous discharges and hydrographs are used for a variety of purposes, such as the design of bridges, culverts, flood-control structures; and the management and regulation of floodplains. fuller (1914), developed a flood-frequency formula based on analysis of flood peaks in hundred of streams to provide simple methods of estimating maxi...