Filter Bank Approach Research Articles

Nonlinear and adaptive undecimated hierarchical multiresolution analysis for real valued discrete time signals via empirical mode decomposition approach

Hierarchical multiresolution analysis is an important tool for the analysis of signals. Since this multiresolution representation provides a pyramid like framework for representing signals, it can extract signal information effectively via levels by levels. On the other hand, a signal can be nonlinearly and adaptively represented as a sum of intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD) algorithm. Nevertheless, as the IMFs are obtained only when the EMD algorithm converges, no further iterative sifting process will be performed directly when the EMD algorithm is applied to an IMF. As a result, the same IMF will be resulted and further level decompositions of the IMFs cannot be obtained directly by the EMD algorithm. In other words, the hierarchical multiresolution analysis cannot be performed via the EMD algorithm directly. This paper is to address this issue by performing a nonlinear and adaptive hierarchical multiresolution analysis based on the EMD algorithm via a frequency domain approach. In the beginning, an IMF is expressed in the frequency domain by applying discrete Fourier transform (DFT) to it. Next, zeros are inserted to the DFT sequence and a conjugate symmetric zero padded DFT sequence is obtained. Then, inverse discrete Fourier transform (IDFT) is applied to the zero padded DFT sequence and a new signal expressed in the time domain is obtained. Actually, the next level IMFs can be obtained by applying the EMD algorithm to this signal. However, the lengths of these next level IMFs are increased. To reduce these lengths, first DFT is applied to each next level IMF. Second, the DFT coefficients of each next level IMF at the positions where the zeros are inserted before are removed. Finally, by applying IDFT to the shorten DFT sequence of each next level IMF, the final set of next level IMFs are obtained. It is shown in this paper that the original IMF can be perfectly reconstructed. Moreover, computer numerical simulation results show that our proposed method can reach a component with less number of levels of decomposition compared to that of the conventional linear and nonadaptive wavelets and filter bank approaches. Also, as no filter is involved in our proposed method, there is no spectral leakage in various levels of decomposition introduced by our proposed method. Whereas there could be some significant leakage components in the various levels of decomposition introduced by the wavelets and filter bank approaches.

A quasi-local method for instantaneous frequency estimation with application to structural magnetic resonance images.

Spatially-varying signal content can be effectively modeled using amplitude modulation-frequency modulation (AM-FM) representations. The AM-FM representation allow us to extract instantaneous amplitude (IA) and instantaneous frequency (IF) components that can be used to measure non-stationary content in biomedical images and videos. This paper introduces a new method for estimating the IA and the IF based on a quasi-local method (QLM). We provide an extensive comparison of AM-FM demodulation approaches based on QLM and a quasi-eigenfunction approximation method using three different filter-banks: (i) a separable, equiripple design, (ii) a Gabor filter bank, and (iii) a directional filter bank approach based on the Contourlet transform. The results document that the use of the new QLM method with an equiripple filter bank design gave the best IF magnitude estimates for a synthetic image. The new QLM method is then applied to a multi-site schizophrenia dataset (N=307). The dataset included structure magnetic resonance images from healthy controls and patients diagnosed with schizophrenia. The IF magnitude is shown to be less sensitive to variations across sites as opposed to the standard use of SMRI images that suffered from significant dependency on the scanner configurations on different collection sites. Furthermore, the regions of interest identified through the use of the IF magnitude are in agreement with previous studies.

Improved Filter Bank Approach for the Design of Variable Bandedge and Fractional Delay Filters

The paper proposes an optimization technique for the design of variable digital filters with simultaneously tunable bandedge and fractional delay using a fast filter bank (FFB) approach. In the FFB approach, full band signals are split into multibands, and each band is multiplied by a proper phase shift to realize the variable fractional delay. In the proposed technique, in the formulation of the optimization of the 0th stage prototype filter of the FFB, the ripples of the filters in the subsequent stages are all taken into consideration. In addition, a shaping filter is applied to the last retained band of the FFB to form the transition band of the variable filter, such that the transition width of each band in the FFB can be relaxed to reduce the computational complexity. In total three shaping filters, constructed from a prototype filter, can be shared by different bands, so that the extra cost incurred due to the shaping filter is low.

A novel voice conversion approach using admissible wavelet packet decomposition

The framework of voice conversion system is expected to emphasize both the static and dynamic characteristics of the speech signal. The conventional approaches like Mel frequency cepstrum coefficients and linear predictive coefficients focus on spectral features limited to lower frequency bands. This paper presents a novel wavelet packet filter bank approach to identify non-uniformly distributed dynamic characteristics of the speaker. Contribution of this paper is threefold. First, in the feature extraction stage, dyadic wavelet packet tree structure is optimized to involve less computation while preserving the speaker-specific features. Second, in the feature representation step, magnitude and phase attributes are treated separately to rule out on the fact that raw time-frequency traits are highly correlated but carry intelligent speech information. Finally, the RBF mapping function is established to transform the speaker-specific features from the source to the target speakers. The results obtained by the proposed filter bank-based voice conversion system are compared to the baseline multiscale voice morphing results by using subjective and objective measures. Evaluation results reveal that the proposed method outperforms by incorporating the speaker-specific dynamic characteristics and phase information of the speech signal.

Second Order Taylor Polyphase Reconstruction of Periodic-Nonuniform Samples in Time-Interleaved ADCs

This paper focuses on a filter bank approach for reconstructing periodic-nonuniform samples using second order Taylor polyphase decomposition for a four-channel time-interleaved ADC (TIADC). The proposed method is based on a parametric linear least squares approach to find the coefficients of synthesis filters used for signal reconstruction of periodic-nonuniform samples. The coefficients of synthesis filters found by linear least squares approach satisfy the general condition for an alias-free filter bank.

Adaptive Filtering Methods for Identifying Cross-Frequency Couplings in Human EEG

Oscillations have been increasingly recognized as a core property of neural responses that contribute to spontaneous, induced, and evoked activities within and between individual neurons and neural ensembles. They are considered as a prominent mechanism for information processing within and communication between brain areas. More recently, it has been proposed that interactions between periodic components at different frequencies, known as cross-frequency couplings, may support the integration of neuronal oscillations at different temporal and spatial scales. The present study details methods based on an adaptive frequency tracking approach that improve the quantification and statistical analysis of oscillatory components and cross-frequency couplings. This approach allows for time-varying instantaneous frequency, which is particularly important when measuring phase interactions between components. We compared this adaptive approach to traditional band-pass filters in their measurement of phase-amplitude and phase-phase cross-frequency couplings. Evaluations were performed with synthetic signals and EEG data recorded from healthy humans performing an illusory contour discrimination task. First, the synthetic signals in conjunction with Monte Carlo simulations highlighted two desirable features of the proposed algorithm vs. classical filter-bank approaches: resilience to broad-band noise and oscillatory interference. Second, the analyses with real EEG signals revealed statistically more robust effects (i.e. improved sensitivity) when using an adaptive frequency tracking framework, particularly when identifying phase-amplitude couplings. This was further confirmed after generating surrogate signals from the real EEG data. Adaptive frequency tracking appears to improve the measurements of cross-frequency couplings through precise extraction of neuronal oscillations.

Characterization of Dysphonic Voices by Means of a Filterbank-Based Spectral Analysis: Sustained Vowels and Running Speech

This article presents a comparative study of the spectral power distribution for normal and dysphonic voices, both for sustained vowels and running speech. The objective of this study was to find robust cues of dysphonia in spectral domain. For this purpose, recordings from two databases are processed, one of them including both sustained vowels and running speech. Additionally, a new measure of stability is introduced (decorrelation time). The application of this measure to the power spectrum is also tested as a cue of dysphonia. The spectral analysis is done having both an auditory model and the filterbank approach as references to the computation of discrete spectrograms. Results are obtained from three sets of recordings belonging to two different databases. The reported results indicate that only minor differences exist in the shape of the power spectrum of normal and dysphonic voices when performing sustained vowel phonation tasks. However, the calculated band power decorrelation times indicate that power in bands between 2000 and 6400Hz is significantly less stable in dysphonic voices. As for running speech, the stability of spectral power is not such a good indicator of dysphonia, but there is a significant difference between normal and dysphonic voices in the power level of high-frequency bands (above 5300Hz). In addition, this means that sampling rates above 10.6ksps are needed for assessing running speech in spectral domain. Also, the results involving decorrelation times indicate that for short-time spectral analysis, frame rates above 100 frames/s should be preferred.

Characterization of escape times of Josephson junctions for signal detection

The measurement of the escape time of a Josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data. In this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy. More specifically, by exploitation of the sample mean of escape times to perform detection, two resonant regions are identified. At low frequencies there is a stochastic resonance or activation phenomenon, while near the plasma frequency a geometric resonance appears. Furthermore, detection performance in the geometric resonance region is maximized at the prescribed value of the bias current. The naive sample mean detector is outperformed, in terms of error probability, by the optimal likelihood ratio test. The latter exhibits only geometric resonance, showing monotonically increasing performance as the bias current approaches the junction critical current. In this regime the escape times are vanishingly small and therefore performance is essentially limited by measurement electronics. The behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed, and a relationship with the error probability is found. Detectors based on the likelihood ratio test could be employed also to estimate unknown parameters in the applied input signal. As a prototypical example we study the phase estimation problem of a sinusoidal current, which is accomplished by using the filter bank approach. Finally we show that for a physically feasible detector the performances are found to be very close to the Cramer-Rao theoretical bound. Applications might be found, for example, in some astronomical detection problems (where the all-sky gravitational and/or radio wave search for pulsars requires the analysis of nearly sinusoidal long-lived waveforms at very low signal-to-noise ratio) or to analyze weak signals in the subterahertz range (where the traditional electronics counterpart is difficult to implement).

Mixed-Radix Fast Filter Bank Approach for the Design of Variable Digital Filters With Simultaneously Tunable Bandedge and Fractional Delay

A popular technique to design variable fractional delay (VFD) filters or variable bandedge filters is the polynomial based finite impulse response (FIR) filters, where each filter coefficient is approximated as a polynomial of the variable parameter. However, if the filter is required to have both VFD and variable bandedge, the computational complexity becomes very high, because two-dimensional polynomials have to be used, provided that the same polynomial idea is followed. In this paper, a filter bank approach is proposed for the design of VFD filters. The basic idea of the approach is to split the full band signals into subbands and each subband is, respectively, shifted by a phase, which is determined by the required fractional delay. The overall fractional delay is achieved by combining all subbands. Using this technique, the variable bandedge could be incorporated into the VFD filter with trivial extra computations. Design examples show that the proposed technique achieves high performance with low computational complexity.

Instantaneous frequency based spectral analysis of nuclear magnetic resonance spectroscopy data

Nuclear magnetic resonance spectroscopy signals are modelled as a sum of decaying complex exponentials in noise. The spectral analysis of these signals allowing for their decomposition and the estimation of the parameters of the components is crucial to the study of biochemical samples. This paper presents a novel Gabor filterbank/notch filtering instantaneous frequency (IF) estimator, that enables the extraction of weaker and shorter lived exponentials. This new approach is an iterative procedure where a Gabor filterbank is first employed to obtain a reliable estimate of the IF of the strongest component present. The estimated strongest component is then notch filtered, which un-masks weaker components, and the procedure repeated. The performance of this method was evaluated using an artificial signal and compared to the short time Fourier transform, reassigned STFT, and the original Gabor filterbank approach. The results clearly demonstrate its superiority in uncovering weaker signals and resolving components that are very close to one another in frequency. Furthermore, the new method is shown to be more robust than the ITCMP technique at low signal to noise ratios.

Feature Extraction from Subband Brain Signals and Its Classification

This paper considers both the non-stationarity as well as independence/uncorrelated criteria along with the asymmetry ratio over the electroencephalogram (EEG) signals and proposes a hybrid approach of the signal preprocessing methods before the feature extraction. A filter bank approach of the discrete wavelet transform (DWT) is used to exploit the non-stationary characteristics of the EEG signals and it decomposes the raw EEG signals into the subbands of different center frequencies called as rhythm. A post processing of the selected subband by the AMUSE algorithm (a second order statistics based ICA/BSS algorithm) provides the separating matrix for each class of the movement imagery. In the subband domain the orthogonality as well as orthonormality criteria over the whitening matrix and separating matrix do not come respectively. The human brain has an asymmetrical structure. It has been observed that the ratio between the norms of the left and right class separating matrices should be different for better discrimination between these two classes. The alpha/beta band asymmetry ratio between the separating matrices of the left and right classes will provide the condition to select an appropriate multiplier. So we modify the estimated separating matrix by an appropriate multiplier in order to get the required asymmetry and extend the AMUSE algorithm in the subband domain. The desired subband is further subjected to the updated separating matrix to extract subband sub-components from each class. The extracted subband sub-components sources are further subjected to the feature extraction (power spectral density) step followed by the linear discriminant analysis (LDA).

Cyclic spectral analysis of radio pulsars

Cyclic spectral analysis is a signal-processing technique designed to deal with stochastic signals whose statistics vary periodically with time. Pulsar radio emission is a textbook example of this signal class, known as cyclostationary signals. In this paper, we discuss the application of cyclic spectral analysis methods to pulsar data and compare the results with the traditional filterbank approaches used for almost all pulsar observations to date. In contrast to standard methods, the cyclic spectrum preserves phase information of the radio signal. This feature allows us to determine the impulse response of the interstellar medium and the intrinsic, unscattered pulse profile directly from a single observation. We illustrate these new analysis techniques using real data from an observation of the millisecond pulsar B1937+21.

A Low-Complexity Flexible Spectrum-Sensing Scheme for Mobile Cognitive Radio Terminals

Low-complexity and flexible spectrum sensing is one of the challenging tasks in a cognitive radio (CR). Most of the work on energy-detection-based spectrum sensing presented in the literature employ a filter bank (FB) to split the wideband input signal into several subbands and detect the spectrum by computing the energy of subbands. However, for a mobile CR handset, a filter-bank-based spectrum sensing is not an area- and power-efficient scheme. In this paper, a novel spectrum-sensing scheme based on a reconfigurable digital downconverter (RDDC) and a reconfigurable filter based on coefficient decimation is proposed for mobile CR handsets, which has very low complexity and high flexibility compared to conventional FB approaches. The basic idea is to rotate the spectrum using an RDDC and filter the desired portion of the spectrum using the reconfigurable filter, which then results in very low complexity. The implementation results on Virtex-4 field-programmable gate array show that our method offers significant reductions in gate count, power consumption, and delay over conventional discrete Fourier transform FB-based spectrum sensing.

Clock-Jitter-Tolerant Wideband Receivers: An Optimized Multichannel Filter-Bank Approach

Clock jitter is one of the most fundamental obstacles in realizing future generations of wideband receivers. Stringent jitter specifications in the sampling clocks of high-performance single-channel and multichannel time-interleaved analog-to-digital converters severely limit the evolution of baseband receivers. This paper presents an analytical framework for the design of clock-jitter-tolerant low-order multichannel filter-bank receivers, with techniques to dramatically lower the sampling-clock-jitter specifications. Although it is well understood that high-order frequency-channelized receivers provide higher tolerance to sampling jitter, this paper shows that low-order bandwidth-optimized multichannel receivers can achieve similar sampling-jitter tolerance. Additionally, this paper presents design tradeoffs and specifications of an example multichannel receiver that can process a 5-GHz baseband signal with 40 dB of signal-to-noise-ratio using sampling clocks that can tolerate up to 5 prmss clock jitter. In comparison, existing architectures based on time-interleaving require 0.5 prmss clock jitter for the given specifications. This extreme jitter tolerance allows for relaxed design of clocking systems, which averts a major roadblock in future wideband-communication-receiver development and provides the potential to enable several high-data-rate communication applications.

Non-contiguous multicarrier waveforms in practical opportunistic wireless systems

Multicarrier modulation is well suited for future wireless communication systems owing to its ability to opportunistically transmit across unoccupied frequency bands. In addition to multicarrier modulation being able to attain high data rates with a sufficient level of error robustness, it also has the potential to achieve transmission flexibility via the non-contiguous access of wireless spectrum. Since both these approaches are highly relevant not only for the conventional wireless communication systems, but also for radar and navigation applications, in this study, the authors shall investigate them for enabling non-contiguous multicarrier modulation that can be used to facilitate spectrally opportunistic cognitive radio systems. One of the approaches is a variant of orthogonal frequency division multiplexing (OFDM), called non-contiguous OFDM (NC-OFDM), whereas the other approach is based on the non-contiguous version of the filter bank approach non-orthogonal frequency division multiplexing (NOFDM), referred to as non-contiguous NOFDM (NC-NOFDM). The performance of these two approaches is assessed in terms of interference mitigation, which involves the use of actual spectrum measurement data, as well as computational complexity.

Correcting the Bias of Spike Field Coherence Estimators Due to a Finite Number of Spikes

The coherence between oscillatory activity in local field potentials (LFPs) and single neuron action potentials, or spikes, has been suggested as a neural substrate for the representation of information. The power spectrum of a spike-triggered average (STA) is commonly used to estimate spike field coherence (SFC). However, when a finite number of spikes is used to construct the STA, the coherence estimator is biased. We introduce here a correction for the bias imposed by the limited number of spikes available in experimental conditions. In addition, we present an alternative method for estimating SFC from an STA by using a filter bank approach. This method is shown to be more appropriate in some analyses, such as comparing coherence across frequency bands. The proposed bias correction is a linear transformation derived from an idealized model of spike-field interaction but is shown to hold in more realistic settings. Uncorrected and corrected SFC estimates from both estimation methods are compared across multiple simulated spike-field models and experimentally collected data. The bias correction was shown to reduce the bias of the estimators, but add variance. However, the corrected estimates had a reduced or unchanged mean squared error in the majority of conditions evaluated. The bias correction provides an effective way to reduce bias in an SFC estimator without increasing the mean squared error.

Long-Term Forecasting by Wavelet-Based Filter Bank Selections and Its Application

Long-term forecasting of seasonal time series is critical in many applications such as planning business strategies and resolving possible problems of a business company. Unlike the traditional approach that depends solely on dynamic models, Li and Hinich (2002) introduced a combination of stochastic dynamic modeling with filter bank approach for forecasting seasonal patterns using highly coherent(High-C) waveforms. We modify the filter selection and forecasting procedure on wavelet domain to be more feasible and compare the resulting predictor with one that obtained from the wavelet variance estimation method. An improvement over other seasonal pattern extraction and forecasting methods based on such as wavelet scalogram, Holt-Winters, and seasonal autoregressive integrated moving average(SARIMA) is shown in terms of the prediction error. The performance of the proposed method is illustrated by a simulation study and an application to the real stock price data.

Time-Interleaved Analog-to-Digital-Converter Compensation Using Multichannel Filters

Published methods that employ a filter bank for compensating the timing and bandwidth mismatches of an M-channel time-interleaved analog-to-digital converter (TIADC) were developed based on the fact that each sub-ADC channel is a downsampled version of the analog input. The output of each sub-ADC is filtered in such a way that, when all the filter outputs are summed, the aliasing components are minimized. If each channel of the filter bank has N coefficients, the optimization of the coefficients requires computing the inverse of an MN times MN matrix if the weighted least squares (WLS) technique is used as the optimization tool. In this paper, we present a multichannel filtering approach for TIADC mismatch compensation. We apply the generalized sampling theorem to directly estimate the ideal output of each sub-ADC using the outputs of all the sub-ADCs. If the WLS technique is used as the optimization tool, the dimension of the matrix to be inversed is N times N. For the same number of coefficients (and also the same spurious component performance given sufficient arithmetic precision), our technique is computationally less complex and more robust than the filter-bank approach. If mixed integer linear programming is used as the optimization tool to produce filters with coefficient values that are integer powers of two, our technique produces a saving in computing resources by a factor of approximately (100.2N(M- 1)/(M-1) in the TIADC filter design.

A Bark-scale filter bank approach to independent component analysis for acoustic mixtures

Uniform filter bank approach can be considered to perform independent component analysis (ICA) for convolved mixtures. It achieves better separation performance than the frequency domain approach and gives faster convergence speed with less computational complexity than the time domain approach. However, when the uniform filter bank approach is applied to natural audio signals, it provides slower convergence for low frequency subbands and gives inferior separation performance for high frequency subbands. Owing to spectral characteristics of natural signals, we present a filter bank approach that employs a Bark-scale filter bank. In the Bark-scale filter bank, low frequency region is minutely divided, whereas high frequency region has much wider subbands. The Bark-scale filter bank approach shows faster convergence speed than the uniform filter bank approach because it has more whitened inputs in the low frequency subbands. It also improves the separation performance as it has enough data to train adaptive parameters exactly in the high frequency subbands.

Adaptive reduced feedback FLNN filter for active control of nonlinear noise processes

In actual nonlinear active noise control (NANC) systems, there often exist nonlinear distortions in such cases: the primary path may be nonlinear, the reference noise may exhibit nonlinear distortion, and the secondary path may have nonminimum-phase. To solve the problems of nonlinear distortions, two novel feedback adaptive filters based on the functional link neural network (FLNN) for NANC systems with low computational complexity are proposed in this paper, which are a feedback functional link neural network (FFLNN) and a reduced feedback functional link neural network (RFFLNN), respectively. To train the proposed nonlinear filters for NANC systems, a reduced complexity filtered-s least mean square (FSLMS) algorithm using filter bank approach is developed. The analysis of computational complexity shows that the RFFLNN adaptive filter involves less computation as compared to FFLNN and FLNN adaptive filters. Moreover, it is demonstrated through computer simulations for nonlinear noise processes that the RFFLNN adaptive filter outperforms FLNN and FFLNN in term of convergence speed and steady-state error. Furthermore, it is more effective in reducing nonlinear effects in NANC systems than other filters.