Nonstationary Sinusoids Research Articles

A Power-Line Interference Canceler Based on Sliding DFT Phase Locking Scheme for ECG Signals

A power-line interference (PLI) removal method is proposed based on a previously published sliding discrete Fourier transform (SDFT) phase locking scheme (PLL), which extracts the nonstationary sinusoids from the electrocardiogram (ECG) signal. The proposed PLI canceler consists of SDFT PLL as a vital element, which can track the variation in center frequency of the PLI either 50 or 60 Hz. The PLI canceler involves the adaptive sampling frequency control in which the sampling frequency of SDFT filter is adaptively adjusted according to the center frequency variation of the interference. Since the in-phase and quadrature components of SDFT filter can provide instantaneous sinusoidal and cosinusoidal interference signals, the SDFT PLL is capable of tracking amplitude, phase, and frequency of the interference. Additional resonators of different bin indices are augmented with SDFT PLL to handle the dominant odd harmonics of PLI. Furthermore, the SDFT PLL is cascaded with another SDFT bin to eliminate the baseline wander present in the real-time ECG signal. The adaptive PLI canceler based on SDFT PLL offers the tracking capability of variant PLI, attenuation of 40 dB, less acquisition time of 0.2 s for a variant PLI of ±5 Hz, removal of dominant odd harmonics, and baseline wander with expense of sampling frequency. Experimental results prove the efficacy of the proposed method in nonstationary sinusoidal interference extraction. Experimental investigation on SDFT PLL using field programmable gate array demonstrates the feasibility of digital implementation of the proposed algorithm.

Textured image segmentation based on modulation models

We propose an approach for textured image segmentation based on amplitude-modulation frequency-modulation models. An image is modeled as a set of 2-D nonstationary sinusoids with spatially varying amplitudes and spatially varying frequency vectors. First, the demodulation procedure for the models furnishes a high-dimensional output at each pixel. Then, features including texture contrast, scale, and brightness are elaborately selected based on the high-dimensional output and the image itself. Next, a normalization and weighting scheme for feature combination is presented. Finally, simple K-means clustering is utilized for segmentation. The main characteristic of this work provides a feature vector that strengthens useful information and has fewer dimensionalities simultaneously. The proposed approach is compared with the dominant component analysis (DCA)+K-means algorithm and the DCA+ weighted curve evolution algorithm on three different datasets. The experimental results demonstrate that the proposed approach outperforms the others.

Detection of non-stationary sinusoids by using joint frequency reassignment and null-to-null bandwidth

We present a method that efficiently describes non-stationarities by parameterizing spectral peaks in terms of the frequency reassignment operator variation and null-to-null peak bandwidth. This kind of parameterization is designed in such a way to properly deal with situations of low signal-to-noise ratios. In addition, it provides for a strong separation between the sinusoidal and noise peak class in a two-dimensional (2D) feature space. Consequently, the percentage of misclassified spectral peaks is drastically reduced, which significantly simplifies the analysis/synthesis of audio signals in the following processing stages.

A Comparative Evaluation of Techniques for Single-Frame Discrimination of Nonstationary Sinusoids

Many spectral analysis and modification techniques require the separation of sinusoidal from nonsinusoidal signal components of a Fourier spectrum. Techniques exist for the estimation of the parameters of nonstationary sinusoids, and for discriminating these from other components, within a single Fourier frame. We present a comparative study of five methods for sinusoidal discrimination, considering their effectiveness and their computational cost.

Measuring instantaneous frequency of local field potential oscillations using the Kalman smoother

Rhythmic local field potentials (LFPs) arise from coordinated neural activity. Inference of neural function based on the properties of brain rhythms remains a challenging data analysis problem. Algorithms that characterize non-stationary rhythms with high temporal and spectral resolution may be useful for interpreting LFP activity on the timescales in which they are generated. We propose a Kalman smoother based dynamic autoregressive model for tracking the instantaneous frequency (iFreq) and frequency modulation (FM) of noisy and non-stationary sinusoids such as those found in LFP data. We verify the performance of our algorithm using simulated data with broad spectral content, and demonstrate its application using real data recorded from behavioral learning experiments. In analyses of ripple oscillations (100–250Hz) recorded from the rodent hippocampus, our algorithm identified novel repetitive, short timescale frequency dynamics. Our results suggest that iFreq and FM may be useful measures for the quantification of small timescale LFP dynamics.

Frequency-Slope Estimation and Its Application to Parameter Estimation for Non-Stationary Sinusoids

Sinusoidal models are often used for the representa- tion, analysis, or transformation of music or speech signals (Quatieri and McAulay 1986; Amatriain et al. 2002.). An important step that is necessary for obtaining the sinusoidal model lies in estimating the amplitudes, frequencies, and phases of the sinusoids from the peaks of the Discrete Fourier Transform (DFT). The estimation is rather simple provided the signal is stationary. A standard method for this estimation is the quadratically interpolated Fast Fourier Transform (QIFFT) estimator (Abe and Smith 2005). The QIFFT estimator uses the bin at the maximum of each spectral peak together with its two neighbors to establish a second- order poly- nomial model of the log amplitude and unwrapped phase of the peak. The amplitude and frequency estimates of the sinusoid that is related to the spectral peak are then derived from the height and frequency position of the maximum of the polyno- mial. The evaluation of the phase polynomial at the frequency position provides the estimate of the phase of the sinusoid. For non- stationary sinusoids, the parameter esti- mation becomes more diffi cult, because the QIFFT algorithm is severely biased whenever the fre- quency is not constant. The term bias refers to the systematic estimation error, that is, the error of the estimator that exists even if no measurement noise is present. For the partials in natural vibrato signals, the estimation bias of the QIFFT estimator accounts for a signifi cant amount of residual energy (i.e., the energy remaining after subtracting the sinusoidal model from the original signal). This is the major reason for the perceived voiced energy in the resid- ual of vibrato signals. A number of algorithms with low estimation bias for non- stationary sinusoids have been proposed. Algorithms that try to implement a maximum

On sinusoidal modeling of nonstationary signals

In this presentation we are going to give an overview over a number of techniques that have been developed in our group to improve the modeling of musical (nonstationary) signals using sinusoidal models. One of the basic problems with sinusoidal models is the fact that the underlying theory is derived assuming stationary sinusoids, while in the real world all sinusoidal components are non stationary. The two topics that will be covered main are, first a technique that allows to distinguish between nonstationary sinusoidal components, noise and transients, and second a new technique for parameter estimation of nonstationary sinusoids using frequency domain demodulation.

Time changes of solar activity, interplanetary magnetic field and solar wind velocity at the Earth's orbit in different spectral bands

We present the results of our analysis of the spectra of the interplanetary magnetic field (IMF) and the solar wind velocity ( V ) calculated on the basis of measurements near the Earth's orbit for the period 1964–1997, and of the sunspot number W . The major aim is to search for similar features in various frequency bands, with an emphasis on the T ∼ 11 yr period of solar (sunspot) cycle and its harmonics, and on so-called “intermittent” oscillations at periods T ∼ 1.3 yr and T ∼ 150 d . We also extract trends from the data to determine long-period changes of IMF and V . A method of non-linear spectral analysis, which we term “the method of global minimum” (MGM) is used. MGM allows self-consistent identification of trends from data and nonstationary sinusoids and estimation of statistical significance of spectral components. The IMF and W spectra both show the main solar cycle at T = 10.8 yr . In addition, the spectrum of the IMF includes (at 99.8% confidence levels) harmonics of this cycle with periods of 151.3 and 136.5 d. We also detect nonstationary sinusoids at T = 1.3 yr in the spectra of IMF and of V and describe their parameters. The detailed description of the 1.3-yr oscillations in the solar wind is of particular interest in that the oscillations are likely to be connected to variations in the rotation rate with the same period near the base of convection zone of the Sun discovered in SOHO data. The 1.3-yr oscillations are not present in the W spectra. Instead, we find oscillations at T = 1.014 and 0.950 yr and suggest an explanation of their presence. Relation between the variations in the spectra of W and V is not as evident as between W and the IMF, however, it exists. In particular, harmonics of the 10.8-yr solar cycle (e.g., sinusoid at T = 261.7 d ) are present in the spectrum of V . Components in the spectra described by high-amplitude sinusoids with T = 198 ± 5 yr in the IMF spectrum and with T = 54 ± 4 yr in the V spectrum make contributions to the long-term trends in these parameters. The trend of V demonstrates a 55% increase in the solar wind velocity for the period 1964–1997. The IMF trend shows a 45% increase of the IMF magnitude for the same time interval; extrapolation of this temporal variation to the past leads to a doubling of the IMF value during the last 100 yr.

Sinusoidal modeling for nonstationary voiced speech based on a local vector transform

A voiced speech signal can be expressed as a sum of sinusoidal components of which instantaneous frequency and amplitude continuously vary with time. Determining these parameters from the input, the time-varying characteristics are crucial error sources for the algorithms, which assume their stationarity within a local analysis segment. To overcome this problem, a new method is proposed, local vector transform (LVT), which can determine instantaneous frequency and amplitude for nonstationary sinusoids. The method does not assume the local stationarity. The effectiveness of LVT was examined in parameter determination for synthesized and naturally uttered speech signals. The instantaneous frequency for the first harmonic component was determined with an accuracy almost equal to that of the time-corrected instantaneous frequency method and higher accuracy than that of spectral peak-picking, autocorrelation, and cepstrum. The instantaneous amplitude was also determined accurately by LVT while considerable errors were left in the other algorithms. The signal reconstructed from the determined parameters by LVT agreed well with the corresponding component of voiced speech. These results suggest that the method is effective for analyzing time-varying voiced speech signals.

A method of extraction of nonstationary sinusoids

A novel method of extraction of nonstationary sinusoidal signals and estimation of their parameters, namely amplitude, phase and frequency is presented. A set of nonlinear differential equations governs the dynamics of the algorithm. Mathematical proofs of the existence, uniqueness and stability of a periodic orbit of such a dynamical system are given. Performance of the proposed algorithm is demonstrated with the aid of computer simulations and the laboratory verification of its functionality is presented. The proposed algorithm exhibits a high degree of noise immunity and robustness and is shown to have a very simple structure which renders it suitable for both software and hardware implementation.

Fast recursive low-rank linear prediction frequency estimation algorithms

A class of fast recursive low-rank linear prediction algorithms for the tracking of time-varying frequencies of multiple nonstationary sinusoids in noise is introduced. Realizations with O(Nn) and O(Nn/sup 2/) arithmetic operations per time step are described, where N is the model order and n is the number of independent sinusoids. The key step towards an operations count that depends only linearly on the model order is fast eigensubspace tracking, and the property that the coefficients of a high-order N prediction filter itself constitute a perfectly (or almost perfectly) predictable sequence that can be annihilated using a low-order 2n prediction error filter that carries the desired signal frequency information in its roots. In this concept, root tracking is limited to a low-order filter polynomial, even if the overmodeling factor N/n is much larger than 1 for optimal noise suppression. Extraneous roots are not computed explicitly. Detailed simulation results confirm the tracking capabilities of the new algorithms.