Phase-Based Frequency Estimation: A Review

Fowler, M. L., Phase-Based Frequency Estimation: A Review, Digital Signal Processing12 (2002) 590–615This paper provides a review of efficient frequency estimation methods that use only the phases of the signal samples. Such methods continue to attract attention in various applications such as radar, electronic warfare, and next-generation communication systems. We present the details of the basic phase-based method, including its theoretical basis and its performance characterization, and provide an integrated presentation of its threshold behavior. In addition, we review several improvements, implementations, and extensions of the basic method and give some new results and viewpoints. In particular, the paper shows that Kay's method is equivalent to Tretter's method together with a simple phase unwrapping algorithm (thus, Kay's method does not really avoid phase unwrapping errors). We also show that a phase-based method for estimating chirp parameters has an advantage when applied to sinusoids: improved threshold behavior. We present a method that, unlike most of the other phase-based methods, can start processing the signal before knowing the number of samples.     

Development of quality bounds for time and frequency domain models: application to the Shell distillation column

Statistical confidence bounds are developed for frequency response and step response models estimated from process input-output data using the frequency sampling filter model structure. The frequency domain bound is an extension of earlier work by the authors (Arifin et al., Journal of Process Control, 1995, 5, 71–76) and the time domain bound is a new result. These bounds provide the engineer with a measure of the quality of the estimated model, and therefore an indication of which aspects of the model are reliable and which aspects require further improvement. The Shell distillation column benchmark problem introduced by Cott (Journal of Process Control, 1995, 5, 60–70) is used for illustrative purposes.     

Quaternion Fourier Descriptors for the Preprocessing and Recognition of Spoken Words Using Images of Spatiotemporal Representations

This paper presents an application of the quaternion Fourier transform for the preprocessing for neural-computing. In a new way the 1D acoustic signals of French spoken words are represented as 2D signals in the frequency and time domain. These kind of images are then convolved in the quaternion Fourier domain with a quaternion Gabor filter for the extraction of features. This approach allows to greatly reduce the dimension of the feature vector. Two methods of feature extraction are tested. The features vectors were used for the training of a simple MLP, a TDNN and a system of neural experts. The improvement in the classification rate of the neural network classifiers are very encouraging which amply justify the preprocessing in the quaternion frequency domain. This work also suggests the application of the quaternion Fourier transform for other image processing tasks.

Solo instrumental music analysis using the source-filter model as a sound production model considering temporal dynamics

A source-filter model, originally devised to represent a sound production process, has been widely used to estimate both of the source signal which includes pitch information and the synthesis filter which includes vowel information, as from sounds of a speech signal. We use this model to identify instruments by their instrumental sound signal. However, this model suffers from an indeterminacy problem. To resolve it, we employ three elements of the sound: loudness, pitch and timbre. Our assumption is that the source signal is represented by time-varying pitch and amplitude, and the synthesis filter by time-invariant line spectral frequency parameters. We construct a probabilistic model that represents our assumption with an extension of the source-filter model. For learning of model parameters, we employed an EM-like minimization algorithm of a cost function called the free energy. Reconstruction of the spectrum with the estimated source signal and synthesis filter, and instrument identification by using the model parameters of the estimated synthesis filter are performed to evaluate our approach, showing that this learning scheme could achieve simultaneous estimation of the source signal and the synthesis filter.

A Comparative Study of Explicit Frequency and Conventional Signal Representations for Speech Recognition

Krishnan, S., and Rao, P. V. S., A Comparative Study of Explicit Frequency and Conventional Signal Representations for Speech Recognition,Digital Signal Processing6(1996), 249–264.The performance of a speech recognition system depends to a large extent on the signal representation strategy. It is therefore important to evaluate various signal representations, with a view to comparing their relative performance on speech recognition tasks. Various comparative studies have been reported earlier in the literature in this respect. However, these studies are limited to comparing some subsets of representations on different kinds of recognition tasks. In this sense, they preclude a fair comparison of the representations on the same task. In contrast, we attempt here a systematic and fairly comprehensive comparison of signal representations along various dimensions (frequency and amplitude scales, speaker normalization, and two statistical classifiers) on a standard (TIMIT) speech database. This study shows that the line spectrum pair frequency representation augmented with spectral amplitudes yields the best recognition performance.     

Acoustic OFDM system and its extension

This paper presents a method of aerial acoustic communication in which data is modulated using OFDM (Orthogonal Frequency Division Multiplexing) and embedded in regular audio material without significantly degrading the quality of the original sound. It replaces the high frequency band of the audio signal with OFDM carriers, each of which is power-controlled according to the spectrum envelope of the original audio signal. The implemented system enables the transmission of short text messages from loudspeakers to mobile handheld devices at a distance of around 3 m. This paper also provides the subjective assessment results and the transmission performances.

一种基于改进直方图均衡的图像增强方法

针对传统图像增强方法的不足,提出一种基于模拟频域滤波重构直方图均衡的图像增强方法.将频率域滤波的思想引入空间域直方图运算当中,在模拟频率直方图统计中进行频率信息的统计,利用这些频率信息建立模拟频率域坐标,进行模拟频域滤波,对滤波处理后的直方图进行均衡化处理.实验表明:与传统方法相比,该算法优化了灰度级的动态分布范围,能得到更清晰的增强效果,且在图像中没有视觉明显的噪声放大.     

H∞ Filtering for Spatially Interconnected Time‐Delay Systems with Interconnected Chains in Finite Frequency Domains

This paper deals with the problem of delay‐dependent H_∞ filtering for spatially interconnected time‐delay systems (SITSs) with interconnected chains in finite frequency domains. First, a multidimensional (N‐D) hybrid time‐delay Roesser model and a delay‐dependent finite frequency bounded ream lemma (BRL) for SITSs with interconnected chains are proposed. Then, using the obtained delay‐dependent finite frequency BRL, a finite frequency H_∞ filter design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, a practical example is provided to clearly demonstrate the effectiveness of the proposed method.     

On the Performance of Permutation Codes for Multi-User Communication

Permutation coding for multi-user communication schemes that originate from the Fast Frequency Hopping/Multiple Frequency Shift Keying modulation is investigated. Each sender is either passive or sends some signal formed as the concatenation of M elementary signals having M different specified frequencies. There is also a jammer, who can introduce disturbances. A single disturbance is either sending the signal that contains all M frequencies at a certain time instant or sending some elementary signal at all time instants. Each receiver receives a vector of M sets, where a set at each time instant contains a fixed frequency if and only if the corresponding elementary signal was sent by either some sender or the jammer. The task of the receiver is to uniquely decode the message of his sender. We present regular constructions of permutation codes for this scheme given the following parameters: the number of frequencies, number of pairs (sender, receiver), number of messages per sender, and maximum number of disturbances of the jammer.     

Frequency domain state feedback and estimation!

The primary purpose of this paper is to present a frequency domain compensation scheme which is completely analogous to the time domain (state-space) employment of a Luenberger state estimator for approximating a linear state variable feedback (l.s.v.f.) design. To accomplish this objective we (i) employ a ‘ factorization ’ of the rational transfer matrix, T(s), of a given system as the product R(s)P(s)^?1, where R(s) and R(s) are ‘ relatively right prime ’ polynomial matrices, (ii) present a frequency domain characterization of l.s.v.f. in terms of its effect on T(s) (actually on R(s) and P(s)), and (iii) extend the notion of the classical ‘ eliminant matrix ’ of two polynomials and its determinant, the ‘ resultant ’, to the matrix case. An example is employed to illustrate the various steps involved and some comparisons are then made to other related investigations.     

On-line learning and modulation of periodic movements with nonlinear dynamical systems

The paper presents a two-layered system for (1) learning and encoding a periodic signal without any knowledge on its frequency and waveform, and (2) modulating the learned periodic trajectory in response to external events. The system is used to learn periodic tasks on a humanoid HOAP-2 robot. The first layer of the system is a dynamical system responsible for extracting the fundamental frequency of the input signal, based on adaptive frequency oscillators. The second layer is a dynamical system responsible for learning of the waveform based on a built-in learning algorithm. By combining the two dynamical systems into one system we can rapidly teach new trajectories to robots without any knowledge of the frequency of the demonstration signal. The system extracts and learns only one period of the demonstration signal. Furthermore, the trajectories are robust to perturbations and can be modulated to cope with a dynamic environment. The system is computationally inexpensive, works on-line for any periodic signal, requires no additional signal processing to determine the frequency of the input signal and can be applied in parallel to multiple dimensions. Additionally, it can adapt to changes in frequency and shape, e.g. to non-stationary signals, such as hand-generated signals and human demonstrations.

光泵磁敏传感器中FPGA调频器设计与实现

射频场调频器是氦光泵磁敏传感器核心驱动部件。模拟压控振荡式调频器存在频率不稳、调试困难和需要高精度测频电路等问题,集成芯片调频器存在控制复杂和功耗高等不足,而FPGA调频器具有频率稳定度高、不需要高精度测频电路和集成在FPGA控制器里的优点。提出氦光泵磁敏传感器数字检测原理和调频器技术指标,阐述FPGA调频器原理并完成设计。调频信号解调实验和扫频式磁共振信号检测实验的结果表明FPGA调频器满足氦光泵磁敏传感器数字化检测要求。     

自适应频率测量方法(AMF)及其在涡街流量计中的应用

本文研究了用于涡街流量计信号处理的自适应频率测量方法(AMF).这种方法将自适应滤波和功率谱分析结合在一起,特别适合于测量或估计涡街流量计这类受随机噪声和干扰影响了的信号频率.理论分析和实验结果证明,此法对提高涡街流量计应用中的测量精度是有效的,同时,也适用于其他仪表测量系统.     

An image rectification scheme and its applications in RST invariant digital image watermarking

This paper presents an image rectification scheme that can be used by any image watermarking algorithm to provide robustness against rotation, scaling and translation (RST) transformations. Rotation and scaling transformations in the spatial domain result in cyclically translational shifts in the log-polar mapping (LPM) of the magnitude of the Fourier transform spectrum of an image. We cut a small block from the LPM domain as a matching template. A new filtering method is proposed to compute the cross-correlation between this template and the magnitude of the LPM of the image having undergone RST transformations to detect the rotation and scaling parameters. We employ the same strategy in the spatial domain to detect the translational parameters in the spatial domain. The scheme can also be used to detect image flipping. The cost of the templates is low and the templates can even be compressed. The detection accuracy for rotation, scaling and translation is also presented. We compare the matching results for the different filters and their performance by the three criteria: signal-to-noise ratio (SNR), peak-to-correlation energy (PCE), and Horner efficiency. We demonstrate that our phase-only filtering method is the only one that can be used in the LPM domain. We also introduce three applications for this rectification scheme and give their experimental results.

Tunability of bulk acoustic wave solidly mounted resonators using passive elements: Concept,design and implementation

This paper presents the impedance behavior of the bulk acoustic wave solidly mounted resonators (BAW‐SMR). Also, it shows the effects of the addition of passive elements (L, C) to this type of resonators. In addition, this article presents a tunable BAW‐SMR filter realized in a ladder topology used for the 802.11b/g standard (2.40–2.48 GHz). Mainly, the filter fulfills the requirements for the WLAN 802.11 b/g standard, presenting a measured ?3.3 dB of insertion loss, –12.7 dB of return loss and selectivity higher than 33 dB at ±30 MHz of the bandwidth. This tunable BAW‐SMR filter has reduced dimensions (1035 × 1075 μm²). Moreover, we show how to shift the center frequency of this tunable filter toward higher and lower frequencies by adding passive elements. Measured shifts of ?1.3% of the center frequency (2.44 GHz) toward lower frequency and +0.6% of the center frequency toward higher frequencies are obtained. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

A Model-Based Frequency Constraint for Mining Associations from Transaction Data

Mining frequent itemsets is a popular method for finding associated items in databases. For this method, support, the co-occurrence frequency of the items which form an association, is used as the primary indicator of the associations's significance. A single, user-specified support threshold is used to decided if associations should be further investigated. Support has some known problems with rare items, favors shorter itemsets and sometimes produces misleading associations. In this paper we develop a novel model-based frequency constraint as an alternative to a single, user-specified minimum support. The constraint utilizes knowledge of the process generating transaction data by applying a simple stochastic mixture model (the NB model) which allows for transaction data's typically highly skewed item frequency distribution. A user-specified precision threshold is used together with the model to find local frequency thresholds for groups of itemsets. Based on the constraint we develop the notion of NB-frequent itemsets and adapt a mining algorithm to find all NB-frequent itemsets in a database. In experiments with publicly available transaction databases we show that the new constraint provides improvements over a single minimum support threshold and that the precision threshold is more robust and easier to set and interpret by the user.

Using the Shape Gradient for Active Contour Segmentation: from the Continuous to the Discrete Formulation

A variational approach to image or video segmentation consists in defining an energy depending on local or global image characteristics, the minimum of which being reached for objects of interest. This study focuses on energies written as an integral on a domain of a function which can depend on this domain. The derivative of the energy with respect to the domain, the so-called shape derivative, is a function of a velocity field applied to the domain boundary. For a given, non-optimal domain, the velocity should be chosen such that the shape derivative is negative, thus indicating a way to deform the domain in order to decrease its energy. Minimizing the energy through an iterative deformation process is known as the active contour method. In the continuous framework, setting the velocity to the opposite of the gradient associated with the L ² inner product is a common practice. In this paper, it is noted that the negativity of the shape derivative is not preserved, in general, by the discretization of this velocity required by implementation. In order to guarantee that the negativity condition holds in the discrete framework, it is proposed to choose the velocity as a linear combination of pre-defined velocities. This approach also gives more flexibility to the active contour process by allowing to introduce some a priori knowledge about the optimal domain. Some experimental results illustrate the differences between the classical and the proposed approach.

Ultra-fast Lensless Computational Imaging through 5D Frequency Analysis of Time-resolved Light Transport

Light transport has been analyzed extensively, in both the primal domain and the frequency domain. Frequency analyses often provide intuition regarding effects introduced by light propagation and interaction with optical elements; such analyses encourage optimal designs of computational cameras that efficiently capture tailored visual information. However, previous analyses have relied on instantaneous propagation of light, so that the measurement of the time dynamics of light–scene interaction, and any resulting information transfer, is precluded. In this paper, we relax the common assumption that the speed of light is infinite. We analyze free space light propagation in the frequency domain considering spatial, temporal, and angular light variation. Using this analysis, we derive analytic expressions for information transfer between these dimensions and show how this transfer can be exploited for designing a new lensless imaging system. With our frequency analysis, we also derive performance bounds for the proposed computational camera architecture and provide a mathematical framework that will also be useful for future ultra-fast computational imaging systems.     

Several digital realizations of two-dimensional E-filters applied to image processing

This paper presents several digital implementations for two-dimensional E-filters. The E-filter is based on a non-linear transformation into the spatial domain. Its response is essentially independent of the frequency of the incoming signal under certain conditions, but depends largely on the digital amplitude. Several digital realizations and attendant problems are presented for E-filters applied to biomedical images obtained from an Anger scintillation camera. The associated sensitivity of the digital E-filter to changes of its parameters is examined. A two-dimensional linear filter is realized by the use of a bi-cubic spline interpolation scheme. The boundary detection of unprocessed and filtered images is also investigated using the hexagonal Golay transform. Several examples of abnormal heart and brain-scans are presented including the filtered images and bounded areas of infarcted and abnormal tissue.     

A Finite Frequency Approach to H∞ Filtering for T–S Fuzzy Systems with Unknown Inputs

This paper deals with the problem of state estimation of T–S fuzzy systems subject to unknown inputs. The proposed observer is designed in finite frequency domain to reduce the conservatism generated by those designed in the entire frequency domain when the unknown input frequency ranges are known beforehand. First, a finite frequency H_∞ index is introduced to measure the robustness against unknown inputs. Then, design conditions are derived in linear matrix inequality terms. Finally, an illustrative example is introduced to check the developed methodology.