Frequency Band Decomposition Research Articles

A Variational Mode Decomposition Analysis and Prediction Simulation of DO in the Water Environment of the Chengdu Area, China

DO is an important index to characterize environmental water quality. The time series fluctuation of DO can be analyzed via frequency band decomposition, which is very valuable for water quality simulations. In this paper, DO in the Chengdu area of China was studied using variational mode decomposition with daily meteorological data and water quality data from 2020 to 2022. After variable decomposition, the DO data were first decomposed into different frequency band signals named IMF1, IMF2, IMF3, IMF4, and IMF5. IMF1 represented the low-frequency signal with long-term trend characteristics of the data. IMF2 to IMF5 represented the high-frequency signal with short-term mutation characteristics of the data. By combining the variable decomposition results with the correlation analysis, it was found that the long-term trend characteristics of DO are affected by the superposition of meteorological factors, hydrological factors, and water pollution factors but have a weak correlation with any single determining factor. The air temperature, water temperature, phosphorus, air pressure, pH value, chemical oxygen demand, and nitrogen were relatively strongly correlated with the long-term trend characteristics of DO. The short-term mutation characteristics of DO were mainly determined using the characteristics of the water body itself, while the influence of the meteorological factors could basically be ignored. The water temperature, pH value, and eutrophication were the biggest influencing factors. Then, a predictive framework combining frequency division with a deep learning model or a machine learning model was constructed to predict DO. The predicted results of GRU, random forest, and XGBoost with and without the framework were compared. It was shown that, after removing the interference factors with correlations less than 0.3, the predicted value of DO was much closer to the actual value. The XGBoost and random forest models with decomposed signals had a high degree of simulation fitting and could be used to predict DO in the Chengdu area. The above research approach can be applied to further explore the prediction of various pollution factors in different areas of China.

Teager Energy Entropy Ratio of Wavelet Packet Transform and Its Application in Bearing Fault Diagnosis.

Kurtogram can adaptively select the resonant frequency band, and then the characteristic fault frequency can be obtained by analyzing the selected band. However, the kurtogram is easily affected by random impulses and noise. In recent years, improvements to kurtogram have been concentrated on two aspects: (a) the decomposition method of the frequency band; and (b) the selection index of the optimal frequency band. In this article, a new method called Teager Energy Entropy Ratio Gram (TEERgram) is proposed. The TEER algorithm takes the wavelet packet transform (WPT) as the signal frequency band decomposition method, which can adaptively segment the frequency band and control the noise. At the same time, Teager Energy Entropy Ratio (TEER) is proposed as a computing index for wavelet packet subbands. WPT has better decomposition properties than traditional finite impulse response (FIR) filtering and Fourier decomposition in the kurtogram algorithm. At the same time, TEER has better performance than the envelope spectrum or even the square envelope spectrum. Therefore, the TEERgram method can accurately identify the resonant frequency band under strong background noise. The effectiveness of the proposed method is verified by simulation and experimental analysis.

Intelligent Transient Overvoltages Location in Distribution Systems Using Wavelet Packet Decomposition and General Regression Neural Networks

Overvoltages are the main causes of damages and accidents in electric power grids. The traditional approach is to install some static protection devices that are passive and cannot identify the overvoltage types or locate where the overvoltage event occurs. In recent years, with the development of smart grids, some online overvoltage monitoring systems have been developed. However, the approaches to data processing still need further development. A novel technique for identification and location of overvoltages in power distribution systems is proposed, which uses capacitor bank energization overvoltages (CBOVs) and ground fault temporary overvoltages (TOVs) as the study cases. The wavelet packet decomposition (WPD) theory is used for frequency band decomposition, and a general regression neural network (GRNN) is used in identification and location. Simulation results based on real-world power distribution systems show that the method is accurate and fast.

PROGRAMMABLE PARALLEL FBD SIGMA DELTA ADC RECONSTRUCTION STAGE DESIGN FOR SOFTWARE DEFINED RADIO RECEIVER

Today’s bottleneck of signal processing in multistandard software defined radio (SDR) receiver is the analog-to-digital converter (ADC). Therefore, the authors present in this paper the design and simulation results of a programmable parallel frequency band decomposition (FBD) architecture for ADC. The designed parallel architecture is composed of six parallel branches based on discrete-time (DT) 4th order sigma delta modulators using single-bit quantizers. Each branch processes a sub-bandwidth of the received signal. Only needed branches are selected according to the chosen standard. The parallel sigma delta modulators’ outputs are handled by a demodulation-based digital reconstruction stage in order to provide the FBD sigma delta-based ADC output signal. The digital reconstruction stage differs from one communication standard to another. In this paper, its design is discussed for the UMTS use case. The objective is to propose a digital reconstruction design with optimized complexity. In fact, the authors propose a comparative study between some configurations of demodulation, decimation and filtering processes. Technical choices and simulation results are discussed. For UMTS use case, the proposed FBD sigma delta-based ADC architecture ensures a computed signal-to-noise ratio (SNR) over 74 dB.

Mixed baseband architecture based on FBD ΣΔ–based ADC for multistandard receivers

<p>This paper presents the design and simulation results of a novel mixed baseband stage for a frequency band decomposition (FBD) analog-to-digital converter (ADC) in a multistandard receiver. The proposed FBD-based ADC architecture is flexible with programmable parallel branches composed of discrete time (DT) 4<sup>th</sup> order single-bit Sigma-Delta modulators. The mixed baseband architecture uses a single non-programmable anti-aliasing filter (AAF) avoiding the use of an automatic gain control (AGC) circuit. System level analysis proved that the proposed FBD architecture satisfies design specifications of the software defined radio (SDR) receiver. In this paper, the authors focus on the Butterworth AAF filter design for a multistandard receiver. Besides, theoretical analysis of the reconstruction stage for UMTS test case is discussed. It leads to a complicated system of equations and high digital filter orders. To reduce the digital reconstruction stage complexity, the authors propose an optimized digital reconstruction stage architecture design. The demodulation-based digital reconstruction stage using two decimation stages has been implemented using MATLAB/SIMULINK. Technical choices and performances are discussed. The computed signal-to-noise ratio (SNR) of the MATLAB/SIMULINK FBD ADC model is equal to at least 75 dB which satisfies the dynamic range required for UMTS signals. Next to hardware implementation with quantized filters coefficients, the authors implemented their proposition in VHDL in a SysGen environment. The measured SNR of the hardware implementation is equal to 74.08 dB which satisfies the required dynamic range of UMTS signals.</p>

Normalizing computed tomography data reconstructed with different filter kernels: effect on emphysema quantification.

ObjectivesTo propose and evaluate a method to reduce variability in emphysema quantification among different computed tomography (CT) reconstructions by normalizing CT data reconstructed with varying kernels.MethodsWe included 369 subjects from the COPDGene study. For each subject, spirometry and a chest CT reconstructed with two kernels were obtained using two different scanners. Normalization was performed by frequency band decomposition with hierarchical unsharp masking to standardize the energy in each band to a reference value. Emphysema scores (ES), the percentage of lung voxels below -950 HU, were computed before and after normalization. Bland-Altman analysis and correlation between ES and spirometry before and after normalization were compared. Two mixed cohorts, containing data from all scanners and kernels, were created to simulate heterogeneous acquisition parameters.ResultsThe average difference in ES between kernels decreased for the scans obtained with both scanners after normalization (7.7 ± 2.7 to 0.3 ± 0.7; 7.2 ± 3.8 to -0.1 ± 0.5). Correlation coefficients between ES and FEV1, and FEV1/FVC increased significantly for the mixed cohorts.ConclusionsNormalization of chest CT data reduces variation in emphysema quantification due to reconstruction filters and improves correlation between ES and spirometry.Key Points• Emphysema quantification is sensitive to the reconstruction kernel used.• Normalization allows comparison of emphysema quantification from images reconstructed with varying kernels.• Normalization allows comparison of emphysema quantification obtained with scanners from different manufacturers.• Normalization improves correlation of emphysema quantification with spirometry.• Normalization can be used to compare data from different studies and centers.

Source ranging based on frequency band decomposition and distance weighting using a single acoustic vector sensor in shallow water

A novel method is proposed for the passive source range estimation based on union processing of pressure and particle horizontal velocity. Autocorrelation functions’ warping spectra of pressure and particle velocities have frequency invariability. The spectra of the warped autocorrelation functions of pressure and particle horizontal velocity have the same line spectrum feature, while the spectrum of the warped autocorrelation function of particle vertical velocity possesses both line and broadband spectrum features. Moreover, the warped autocorrelation function’s spectrum of particle vertical velocity has more peaks, and the peak width is broader than those of pressure and particle horizontal velocity. In this paper, source ranges are estimated based on frequency band decomposition and distance weighting, and a guided source with a known range is employed to provide the crucial frequency invariant features. Experimental data in shallow water with an iso-speed profile are used to verify the approach which can reasonably estimate source ranges with the relative errors of the source ranging basically less than 7%. This method can effectively reduce the mainlobe width and background level of the cost function, and can significantly improve the resolution of source range estimation, compared with the results of conventional source ranging approach that uses a single pressure hydrophone.

Research on Multi-Frequency Weak Signal Detection Based on Adaptive Flexible Stochastic Resonance

According to the problem that multi-frequency weak signal under the full frequency coverage constraint is hard to detect, this paper puts forward a detection method by adaptive flexible stochastic resonance. Based on frequency band decomposition of input signal, each function modules of flexible stochastic resonance system are configured for different frequency bands. Parameters including system structural parameters, frequency compression factor and frequency of modulation signal are optimized adaptively by genetic algorithm. Then each signal component distributed on each frequency band is processed by stochastic resonance effect to realize the enhancement of multiple weak features under the full frequency coverage constraint. Finally, through simulation analysis and an example of rolling bearing fault diagnosis, the effectiveness and comprehensiveness of this presented method in the detection of multi-frequency weak signal is verified.

Multi-stage noise band cancellation modulator for digitisation of distorted signals

A new sigma-delta modulator (ΣΔM) architecture is proposed to digitise wideband distorted signals. It combines frequency band decomposition with bandpass (BP) ΣΔ converters and cascaded architectures. The novelties are the use of the residual signal transfer function at the output of the first summing node in a classical BP ΣΔ that is an almost free signal shaping in the ΣΔM and the digitisation of the shaped noise in order to cancel it out in a particular band.

A self-calibration scheme for extended frequency-band-decomposition sigma-delta ADC

Frequency-band-decomposition (FBD) is a good candidate to be used to increase the bandwidths of ADC converters based on sigma-delta modulators for software and cognitive radio applications where we need to convert wide bandwidths. Each modulator processes a part of the band of the input signal which is then passed through a digital filter. In the case of large mismatches in the analog modulators, a new solution, called extended frequency-band-decomposition (EFBD) can be used. As an example, this solution can allow for a 4% error in the central frequencies without significant degradation of its performance when the digital processing part is paired with the analog modulators. A calibration of the digital part is thus required to reach these theoretical performances. This paper will focus on a self-calibration algorithm for an EFBD. The algorithm helps minimize the quantization noise of the EFBD and helps to flatten the signal transfer function.

Extended frequency-band-decomposition sigma–delta A/D converter

Parallelism can be used to increase the bandwidths of ADC converters based on sigma---delta modulators. Each modulator converts a part of the input signal band and is followed by a digital filter. Unfortunately, solutions using bandpass sigma---delta modulators are very sensitive to the position of the modulators' central frequencies. This paper shows the feasibility of a frequency-band-decomposition (FBD) ADC using continuous time bandpass sigma---delta modulators, even in the case of large analog mismatches. The major benefit of such a solution, called extended-frequency-band-decomposition (EFBD) is its low sensitivity to analog parameters. For example, a relative error in the central frequencies of 4% can be accepted without significant degradation in the performance (other published FBD ADCs require a precision of the central frequencies better than 0.1%). This paper will focus on the performance which can be reached with this system, and the architecture of the digital part. The quantization of coefficients and operators will be addressed. It will be shown that a 14 bit resolution can be theoretically reached using 10 sixth-order bandpass modulators at a sampling frequency of 800 MHz which results in a bandwidth of 80 MHz centered around 200 MHz (the resolution depends on the effective quality factor of the filters of the analog modulators).

Efficient solution for frequency band decomposition problem using wavelet packet in HRV

Heart rate variability (HRV) is a very significant noninvasive tool for assessment of sympathovagal balance (SB) that reflects variation of parasympathetic and sympathetic activities in autonomic nervous system (ANS). Low frequency/high frequency (LF/HF) power ratio provides information about these activities. Because of nonstationary characteristic of HRV, analyses based on wavelet transform were typically preferred in previous studies. There is an important problem that required frequency ranges for LF and HF cannot be obtained using discrete wavelet transform (DWT). Different sampling frequencies do not remove this problem. In this study, a solution based on wavelet packet (WP) is presented for removing this problem. In addition, effect of WP on SB values is investigated. Method was applied to spontaneous ventricular tachyarrhythmia database and variation of energy values and LF/HF energy ratios were compared for DWT and WP. WP provides absolutely excellent approximation to required frequency bands and exposes different and impressive SB results.

Multirate Formulation for Mismatch Sensitivity Analysis of Analog-to-Digital Converters That Utilize Parallel -Modulators

A general formulation based on multirate filterbank theory for analog-to-digital converters using parallel sigmadelta modulators in conjunction with modulation sequences is presented. The time-interleaved modulators (TIMs), Hadamard modulators (HMs), and frequency-band decomposition modulators (FBDMs) can be viewed as special cases of the proposed description. The usefulness of the formulation stems from its ability to analyze a system's sensitivity to aliasing due to channel mismatch and modulation sequence level errors. Both Nyquist-rate and oversampled systems are considered, and it is shown how the matching requirements between channels can be reduced for oversampled systems. The new formulation is useful also for the derivation of new modulation schemes, and an example is given of how it can be used in this context.

Subband Finite-State Vector Quantization for Still Image Coding

Subband coding (SBC) with vector quantization (VQ) has been shown to be an effective method for coding images at low bit rates. The basic idea of subband coding is to split up the frequency band of the signal and then to encode the subbands. Reconstruction is performed by decoding and merging the interpolated subband images. In VQ, the image to be encoded is first processed to yield a set of vectors. The input vectors are individually quantized to the closest codewords in the codebook. In this paper, we propose a new subband finite-state vector quantization (SBC-FSVQ) scheme that combines the SBC and the FSVQ. The frequency band decomposition of an image is carried out by means of 2D separable quadrature mirror filters (QMFs). In our coding scheme, we split the image spectrum into sixteen equally sized subbands. The FSVQ is used to improve the performance by using the correlations of the neighboring samples in the same subband. Thus, our SBC-FSVQ scheme not only has the advantages of the SBC-VQ scheme but also reduces the bit rate and improves the image quality. Experimental results are given and comparisons are made using our new schemes and some other coding techniques. Our technique yields good PSNR performance, for images both inside and outside a training set of five 512 × 512 images. In the experiments, it is found that our SBC-FSVQ scheme achieves the best PSNR performance at nearly the same bit rate.

Six-band sub-band coder on ECG waveforms.

An ECG sampled at a rate of 500 samples s-1 or more produces a large amount of redundant data that are difficult to store and transmit. A process is therefore required to represent the signals with clinically acceptable fidelity and with the least code bits possible. In the paper, an efficient sub-band coding method for encoding ECG waveforms is presented. Although sub-band coding has been successfully applied to speech signals, it is the first time that this technique has been applied to the encoding of ECG waveforms. A frequency band decomposition of an ECG waveform is carried out by means of quadrature mirror filters (QMF), which split the ECG spectrum into six bands of unequal width. In the lower frequency bands, which contain most of the ECG spectrum energy, a larger number of bits per sample is used, whereas in upper frequency bands, which contain noise-like signals, fewer bits per sample and the run length coding method are used. The simulation results are presented in terms of bit rates and the quality of the reconstructed waveforms. The results show that a reproduction with an average signal-to-noise ratio (SNR) of 29.97 dB can be achieved even at an average bit rate of 0.81 bits per sample.

Sub‐band coding of digital images

Abstract An efficient sub‐band coding method for encoding images is presented in this paper. In this method a frequency band decomposition of the image is carried out by means of two‐dimensional separable quadrature mirror filters (QMF's), which split the image spectrum into sixteen uniform sub‐bands. In the coding process, we employ special quantizers and encoding algorithms which are designed according to the characteristics (including the visual perceptual property) of the sub‐bands to quantize and to encode these subimages, separately. The simulation results are presented in terms of average bit rates and the quality (in subjective as well as mean squared senses) of the reconstructed images. These results indicate that a good quality reproduction can be achieved at high compression rates. The paper also shows that a seven‐band decomposition has very high performance in quality, compression rate, and economy.

Subband coding of images using vector quantization

A novel two-dimensional subband coding technique is presented that can be applied to images as well as speech. A frequency-band decomposition of the image is carried out by means of 2D separable quadrature mirror filters, which split the image spectrum into 16 equal-rate subbands. These 16 parallel subband signals are regarded as a 16-dimensional vector source and coded as such using vector quantization. In the asymptotic case of high bit rates, a theoretical analysis yields that a lower bound to the gain is attainable by choosing this approach over scalar quantization of each subband with an optimal bit allocation. It is shown that vector quantization in this scheme has several advantages over coding the subbands separately. Experimental results are given, and it is shown the scheme has a performance that is comparable to that of more complex coding techniques. >