重心動揺のスペクトル解析における問題点

The present study aims to establish normal limits of short–term Heart Rate Variability (HRV) indices with the two popular spectral domain methods of Fast Fourier Transform (FFT) and Autoregressive (AR) model in three psychosomatically important age groups of healthy male subjects. The three considered age groups are 18–30 years, 30–45 years and 45–60 years and HRV decreases in the higher age groups when evaluated with both the FFT and AR models. Vagal control becomes weak with the ageing process. However, the corresponding HRV indices computed with both the FFT and AR models differ quantitatively, which may be due to methodological differences. The FFT–based technique evaluates HRV indices on the actual RR interval series length and hence, the HRV indices using this technique are considered to be highly accurate, where as the AR model works on the basis of linear prediction. This study may help towards optimisation of AR models such that the HRV indices calculated with both FFT and AR models are nearly the same.

To apply both autoregressive (AR) and fast Fourier transform (FFT) spectral analysis at rest, during two different dynamic exercise intensities and in recovery from maximal exercise and to compare raw and normalized powers obtained with both methods. Sixteen participants (age 22.3 +/- 4.3 year) performed resting, submaximal and maximal protocols. The submaximal protocol consisted of two 5-min walks at 4 km h(-1) at treadmill grades of 0 and 7.5%. Beat-to-beat R-R series were recorded. FFT and AR analyses were preformed on the same R-R series. Compared to AR, FFT provided higher total power (TP) and raw high-frequency (HF) power at rest and exercise. Furthermore, FFT LF/HF ratio was lower than with the AR, except under resting conditions. Both methods showed reductions in TP, raw HF and LF powers during exercise and recovery. Only the AR revealed a significant reduction for normalized HF power and increase for normalized LF power in transition from rest to exercise conditions. AR and FFT methods are not interchangeable at rest or during dynamic exercise conditions. The AR method is more sensitive to the effects of exercise on the normalized power spectra of heart rate variability (HRV) than FFT. Finally, as both approaches are equally insensitive to the increase of exercise relative intensity, there is no practical advantage of performing HRV spectral analyses by the AR or FFT at higher workloads.

Dominant frequency (DF) of electrophysiological data is an effective approach to estimate the activation rate during Atrial Fibrillation (AF) and it is important to understand the pathophysiology of AF and to help select candidate sites for ablation. Frequency analysis is used to find and track DF. It is important to minimize the catheter insertion time in the atria as it contributes to the risk for the patients during this procedure, so DF estimation needs to be obtained as quickly as possible. A comparison of computation tim- es taken for spectrum estimation analysis is presented in this paper. Fast Fourier Transform (FFT), Blackman-Tukey (BT), Autoregressive (AR) and Multiple Signal Classification (MUSIC) methods are used to obtain the frequency spectrum of the signals. The time to produce DF was measured for each method. The method which takes the shortest time for analysis is selected for real time application purpose.

Speaker and language recognition in noisy and degraded channel conditions continue to be a challenging problem mainly due to the mismatch between clean training and noisy test conditions. In the presence of noise, the most reliable portions of the signal are the high energy regions which can be used for robust feature extraction. In this paper, we propose a front end processing scheme based on autoregressive (AR) models that represent the high energy regions with good accuracy followed by a modulation filtering process. The AR model of the spectrogram is derived using two separable time and frequency AR transforms. The first AR model (temporal AR model) of the sub-band Hilbert envelopes is derived using frequency domain linear prediction (FDLP). This is followed by a spectral AR model applied on the FDLP envelopes. The output 2-D AR model represents a low-pass modulation filtered spectrogram of the speech signal. The band-pass modulation filtered spectrograms can further be derived by dividing two AR models with different model orders (cut-off frequencies). The modulation filtered spectrograms are converted to cepstral coefficients and are used for a speaker recognition task in noisy and reverberant conditions. Various speaker recognition experiments are performed with clean and noisy versions of the NIST-2010 speaker recognition evaluation (SRE) database using the state-of-the-art speaker recognition system. In these experiments, the proposed front-end analysis provides substantial improvements (relative improvements of up to 25%) compared to baseline techniques. Furthermore, we also illustrate the generalizability of the proposed methods using language identification (LID) experiments on highly degraded high-frequency (HF) radio channels and speech recognition experiments on noisy data.

The Burg algorithm for maximum entropy power spectral density estimation is applied to a time series of data obtained from a Michelson interferometer and compared with a standard fast Fourier transform (FFT) estimate for resolution capability. The propane transmittance spectrum was estimated by use of the FFT with a 2(18)-data sample interferogram, giving a maximum unapodized resolution of 0.06 cm(-1). This estimate was then interpolated by zero filling an additional 2(18) points, and the final resolution was taken to be 0.06 cm(-1). Comparison of the maximum entropy method (MEM) estimate with the FFT was made over a 45-cm(-1) region of the spectrum for several increasing record lengths of interferogram data beginning at 2(10). It is found that over this region of 45 cm(-1), the MEM estimate with 2(16) data samples is in close agreement with the FFT estimate using 2(18) samples.

We present a computationally efficient method of calculating confidence intervals for the maximum entropy (ME) or autoregressive (AR) spectrum, based on new theoretical considerations. The method is consistent with the well-known asymptotic results, and it can be incorporated under certain assumptions into the Levinson-Durbin recursion. The method is also extended to ME wavenumber estimation.

Image measurement using pressure-sensitive paint (PSP) is an effective tool for analyzing the unsteady pressure field on the surface of a body in a low-speed air flow, which is associated with wind noise. In this study, the surface pressure fluctuation due to the tonal trailing edge (TE) noise for a two-dimensional NACA 0012 airfoil was quantitatively detected using a porous anodized aluminum PSP (AA-PSP). The emission from the PSP upon illumination by a blue laser diode was captured using a 12-bit high-speed complementary metal-oxide-semiconductor (CMOS) camera. The intensities of the captured images were converted to pressures using a standard intensity-based method. Three image-processing methods based on the fast Fourier transform (FFT) were tested to determine their efficiency in improving the signal-to-noise ratio (SNR) of the unsteady PSP data. In addition to two fundamental FFT techniques (the full data and ensemble averaging FFTs), a technique using the coherent output power (COP), which involves the cross correlation between the PSP data and the signal measured using a pointwise sound-level meter, was tested. Preliminary tests indicated that random photon shot noise dominates the intensity fluctuations in the captured PSP emissions above 200 Hz. Pressure fluctuations associated with the TE noise, whose dominant frequency is approximately 940 Hz, were successfully measured by analyzing 40,960 sequential PSP images recorded at 10 kfps. Quantitative validation using the power spectrum indicates that the COP technique is the most effective method of identification of the pressure fluctuation directly related to TE noise. It is possible to distinguish power differences with a resolution of 10 Pa $$^2$$ (4 Pa in amplitude) when the COP was employed without use of another wind-off data. This resolution cannot be achieved by the ensemble averaging FFT because of an insufficient elimination of the background noise.

This paper deals with multichannel time series of degenerate rank, and extends the maximum entropy method over the degenerate rank case. In order to define the entropy of a multichannel time series of degenerate rank, we must first clarify all the deterministic relationships in the time series. This will be done for any regular time series matching given finite data <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{0}, R_{1},..., R_{n}}</tex> of the autocorrelation sequence <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{k}\}\min{-\infin}{\infin}</tex> . A necessary and sufficient condition of the existence of a regular time series matching the data will be presented. Next, the entropy H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> (P) of a time series with its power spectrum P(ω) of rank less than equal to m is defined by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_{m}(P) =\int{\min{-\pi}\max{\pi}\logS_{m}[P(\omega)] d\omega</tex> where S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> [P] denotes the sum of all the principal minors of order m of the matrix P. The main purpose of this paper is to show that the maximum entropy power spectrum (i.e., the power spectrum which maximizes the entropy) is identical with the autoregressive power spectrum (i.e., the power spectrum obtained by the autoregressive fitting) even in the degenerate rank case.

Background: Parkinson's disease (PD) is a degenerative disease of the brain that often do harm to the motor skills of patients. A disturbed gait is very common among PD patients, who are easy to fall down and may lose their functional independence. Purpose: In this paper, we extract features from the gait signals in PD patients and control subjects for the purpose of comparison and realization of automatic recognition in computer. Also, we want to extract the pattern of walking in PD and help explain the disturbed gait through the perspective of bioinformatics. Method: In this paper, autoregressive (AR) model is applied to analysis of foot-pressure based on Yule-Walker equation for the calculation of power spectra. In the comparison process, we also give our own definition to Associated Discrete Index (ADI) in order to measure the discrete degree at a same frequency. Results: We analyze the data from three research groups: Ga, Ju and Si. The database includes 18, 25, 29 control subjects and 29, 29, 35 PD patients respectively. In the framework of 31-50 Hz in the power spectra of Ga; 7-12 Hz, 25-38 Hz, 43-50 Hz in Ju; and 2-10 Hz in Si, we can see obvious difference between PD patient and control subject through t-test. Conclusions: The AR model can be used as a novel and useful tool to study the time series of foot-pressure. Associated Discrete Index could be an indicator in classification the gait signal in PD patient.

The application of time series analysis to describe the dynamic movements of suspension bridges

In passive narrow-band or broadband target detection sonars, line arrays are used to enhance performance. In large towed arrays, wave-number-frequency (k-ω) data analysis methods have been used on an experimental basis to detect and identify the presence of noise generators. The noise sources are composed of acoustically radiating sources located in the ocean, vibrational energy within the array, and pressure disturbances along the array. In this paper, a hybrid autoregressive (AR) technique is presented that will generate k-ω solutions having better spatial resolution than is currently possible with methods that make use of a two-dimensional fast Fourier transform (FFT). The hybrid AR method is implemented by applying a one-dimensional FFT on the sampled time series data and using this result to obtain an averaged array cross-spectral density matrix. The AR method is now applied to the spatial cross spectral density matrix to obtain a wave-number-frequency spectrum. For the hybrid AR method, equations are presented for calculating the spatial wave-number resolution as a function of signal-to-noise ratio (SNR), array size, and time-bandwidth product (T-BW). The equations for resolution and array gain are useful for determining when to apply the hybrid AR method. In addition to the hybrid AR development, a modification of the FFT–FFT method is introduced that provides efficient and rapid computation of a standard wave-number-frequency spectrum. Comparisons for various SNR, AR order, and T-BW conditions using computer simulated, and actual at-sea data are made between the k-ω solutions obtained using this modified FFT method and our proposed hybrid AR technique.

In this paper, a method of analysis attention state based on the time series transformed by the improved k nearest neighbour network is proposed. In the proposed method, counting number state EEG signals and closing eyes state EEG signals are constructed into networks by the improved k nearest neighbour network respectively, and each networks are converted into time series, which are compared with original EEG time series by means of analysis of power spectrum. The results show that studying power spectrum of time series from network is more easily than original time series to distinguish between counting number state EEG signals and closing eyes state EEG signals. We confirmed that the proposed method could be of practical use.

Potential fluctuation during early stage of stress corrosion cracking of type-304 stainless steel in chloride solution

A neural net algorithm for multidimensional maximum entropy spectrum estimation

Atrial fibrillation (AFib) is the most common cardiac arrhythmia. Areas in atrial tissue with complex fractionated atrial electrograms (CFAEs) are among others responsible for the maintenance of AFib. Those areas are ideal target sites for ablation to eliminate AFib and restore sinus rhythm. As CFAEs are associated with high fibrillatory frequency, automated identification of CFAEs with spectral analysis helps developing objective strategies for AFib ablation. While the application of current techniques is restricted, this paper introduces a new approach to determine characteristic frequencies during AFib. By using Teager's energy operator we calculate the signal envelope and study its spectrum after Fast Fourier Transformation. Harmonic analysis of distinctive peaks in the power spectrum is carried out to assess characteristic frequencies of a CFAE. While the currently available methods only find one dominant frequency in the spectrum of the signal, our method is capable to find multiple characteristic frequencies, if present. Since it is believed that during AFib the atrium is activated by one or multiple wavelets, our method opens new opportunities for investigation of multiple wavelets propagation.