Frequency Interpolation Research Articles

A Real Time Power System Harmonic Estimator Considering Fundamental Frequency Variations

A new technique based on orthogonal filters and iterative frequency tracking is proposed to estimate harmonic components in power systems for real time applications. Frequency interpolation is used to estimate fundamental frequency and harmonics when the nominal frequency of the signal is a non-integer value. Fixed data window size and fixed sampling rate are the two advantageous features of the proposed technique. An off-line computation method with linear interpolation is proposed to reduce the number of computations involved during the generation of filter coefficients. The proposed technique was implemented using a real-time DSP (digital signal processor) data acquisition system. The performance of the proposed technique was studied by estimating the harmonic components of various signals. A FFT (Fast Fourier Transform) based technique was also used to estimate harmonic components for comparison. It has been shown that the accurate fundamental frequency is computed using iterative technique, and then accurate harmonic components are estimated when the fundamental frequency is not equal to the power system nominal frequency.

Dynamic Spectral Envelope Modeling for Timbre Analysis of Musical Instrument Sounds

We present a computational model of musical instrument sounds that focuses on capturing the dynamic behavior of the spectral envelope. A set of spectro-temporal envelopes belonging to different notes of each instrument are extracted by means of sinusoidal modeling and subsequent frequency interpolation, before being subjected to principal component analysis. The prototypical evolution of the envelopes in the obtained reduced-dimensional space is modeled as a nonstationary Gaussian Process. This results in a compact representation in the form of a set of prototype curves in feature space, or equivalently of prototype spectro-temporal envelopes in the time-frequency domain. Finally, the obtained models are successfully evaluated in the context of two music content analysis tasks: classification of instrument samples and detection of instruments in monaural polyphonic mixtures.

Silicon Resonator Based 3.2 $\mu$W Real Time Clock With $\pm$10 ppm Frequency Accuracy

This paper presents an ultra-low power generic compensation scheme that is used to implement a real time clock based on an AlN-driven 1 MHz uncompensated silicon resonator achieving 3.2 μW power dissipation at 1 V and ±10 ppm frequency accuracy over a 0-50°C temperature range. It relies on the combination of fractional division and frequency interpolation for coarse and fine tuning respectively. By proper calibration and application of temperature dependent corrections, any frequency below that of the uncompensated resonator can be generated yielding programmability, resonator fabrication tolerances and temperature drift compensation without requiring a PLL. To minimize the IC area, a dual oscillator temperature measurement concept based on a ring oscillator/resistor thermal sensor was implemented yielding a resolution of 0.04°C. The IC was fabricated on a 0.18 μm 1P6M CMOS technology.

Flutter Equation as a Piecewise Quadratic Eigenvalue Problem

F LUTTER is a dynamic aeroelastic stability problem which is usually analyzed by solving a nonlinear eigenvalue problem. Most existing solution methods are characterized by two distinct features, namely the interpolation of frequency–domain aerodynamic loads and an iteration procedure to solve the eigenvalue problem. The proposed approach exploits the properties of a C continuous load interpolation scheme to solve the flutter eigenvalue problem without iteration. Pitt [1] presented a noniterative scheme where the solutions of the linearized eigenvalue problem at fixed reduced frequencies are interpolated to other frequencies, which yields a computationally efficient procedure. However, that approach does not include means to determine the accuracy of the solutions obtained, and it requires a mode tracking procedure which can become fairly involved for complex cases with hundreds of modes. Back and Ringertz [2] eliminate the need for mode tracking and achieve a given accuracy, but their method requires iteration. Goodman [3] solves the flutter equation as a piecewise quadratic eigenvalue problem (QEP) as it is proposed here. Because of the type of interpolation used, the roots obtained thus are not continuous between segment boundaries. This problem is addressedwith the interpolation scheme described below. In the next section, the eigenvalue problem is presented, followed by a description of the interpolation method. Finally, a solution procedure based on this interpolation scheme is discussed.

Localized Mode DFT-S-OFDMA Implementation Using Frequency and Time Domain Interpolation

This paper presents a novel method to generate a localized mode single-carrier frequency division multiple access (SC-FDMA) waveform. Instead of using DFT-spread OFDMA (DFT-S-OFDMA) processing, the new structure called SCiFI-FDMA relies on frequency and time domain interpolation followed by a user-specific frequency shift. SCiFI-FDMA can provide signal waveforms that are compatible to DFT-S-OFDMA. In addition, it provides any resolution of user bandwidth allocation for the uplink multiple access with comparable computational complexity, because the DFT is avoided. Therefore, SCiFI-FDMA allows a flexible choice of parameters appreciated in broadband mobile communications in the future.

NUFFT-Based Iterative Reconstruction Algorithm for Synthetic Aperture Imaging Radiometers

Synthetic aperture imaging radiometers (SAIRs) are powerful sensors for high-resolution observation of the Earth at low microwave frequencies. However, the future application of this new technology is limited by its large number of element antennas and receiving channels. In order to further reduce the complexity of the whole system, the circular and rotating array configurations have been proposed. Their disadvantages lie primarily in more complicated image reconstruction, because the conventional fast Fourier transform (FFT) method could not be used directly for image reconstruction. This letter introduces an iterative method for the reconstruction of radiometric brightness temperature maps from nonuniform visibility function samples. This method combines the conjugate gradient algorithm with min-max nonuniform FFT approach, which has been shown to provide considerably improved image quality relative to the traditional gridding method. Simulations for SAIRs were performed and showed better image quality in comparison to the traditional frequency interpolation method.

Frequency Interpolation of the Electromagnetic Surface Currents Via Singular Value Decomposition. Application to High-Frequency Analysis

The time-harmonic electromagnetic scattering from conducting surfaces is considered. In this context, a recently published model order reduction for frequency interpolation of the surface current via singular value decomposition (SVD) is analyzed and evaluated: the exact currents computed at <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> frequencies are arranged columnwise in a matrix, the SVD of which provides an orthonormal basis; on account of the observed exponential decrease of the singular values of this matrix, it is assumed that the dimension of the basis required for an accurate interpolation is much smaller than the number of unknowns in the original formulation. We propose in this paper a formal framework that justifies this decrease of the singular values, as well as the corresponding behavior of the interpolation error made on the current. From considerations based on high-frequency electromagnetics, it is shown that this method can be interpreted in terms of sampling criteria for the current, that yield an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> estimate for the minimum value of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> . Numerical examples illustrate the capacities of this technique for frequency interpolation and for high-frequency analysis of the currents.

Evaluation of a new gridding method for fully 3D direct Fourier PET reconstruction based on a two-plane geometry

This study investigated how the choice of fixed planes for the representation of the projection data of a cylindrical positron emission tomography (PET) scanner simplifies the frequency interpolation required by the 3D Fourier slice theorem (3D-FST). A new gridding algorithm based on a two-plane geometry and requiring only 1D interpolations in the Fourier domain was compared with the direct implementation of the 3D-FST. We show that the use of two orthogonal planes leads to signal to noise ratios similar to those achieved with the 3D-FST algorithm from projection data acquired with up to two times more count rates, while the resolution remains similar.

On the interpolation of the frequency variations of the MoM‐PO impedance matrix over a wide bandwidth

AbstractA possibility of generating wide‐band data from MoM‐PO hybrid formulation by frequency interpolation of the impedance matrix is examined with particular attention given to a simple interpolation scheme originally proposed for the MoM impedance matrix, employing three uniformly spaced frequency nodes forming a sliding window over the desired band. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 738–741, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23190

Updating 3D acoustic models with the constitutive relation error method: A two-stage approach for absorbing material characterization

In the global framework of improving vibro-acoustic numerical simulations together with the need to decrease the number of prototyping stages, improving the quality for acoustic models becomes increasingly important for many industries such as automotive companies, for instance. This paper focuses on achieving greater accuracy for acoustic numerical simulations by making use of a parametric updating technique, which enables tuning the model parameters inside physically meaningful boundaries. The improved model is used for the next prototyping stages, allowing more accurate results within reduced simulation times. The updating technique used in this paper is based on recent works dealing with the constitutive relation error (CRE) method applied to acoustics. The updating process focuses on improving the acoustic damping matrix related to the absorbing properties of the materials covering the borders of the acoustic domain. The present study proposes a 2-stage optimization process, which exhibits many advantages. Indeed, the computational time decreases, the frequency interpolation of the material absorbing properties outside the studied frequency range is easily performed, and comparing the correlation of several material absorbing constitutive equations with experimental records is fast. Additional originality of the work comes with the application of the CRE updating method to a concrete real-life device, while previous works addressed purely numerical setups without experimental data. The test-case is the TRICARMO setup engineered by LMS International in Leuven, Belgium. The TRICARMO setup is a simplified car cabin with rigid walls and car seats inside. Thanks to the 2-stage approach, the material property characterization of the seat is improved by running the updating simulation process using a physical absorbing material model.

Frequency Interpolation of Jones Matrices

We estimate the frequency-dependence of the Jones matrix of an optical fiber from its values at several discrete optical frequencies and illustrate our procedures through calculations of higher order polarization-mode dispersion effects in optical fibers

Low Bit-Rate Object Coding of Musical Audio Using Bayesian Harmonic Models

This paper deals with the decomposition of music signals into pitched sound objects made of harmonic sinusoidal partials for very low bit-rate coding purposes. After a brief review of existing methods, we recast this problem in the Bayesian framework. We propose a family of probabilistic signal models combining learned object priors and various perceptually motivated distortion measures. We design efficient algorithms to infer object parameters and build a coder based on the interpolation of frequency and amplitude parameters. Listening tests suggest that the loudness-based distortion measure outperforms other distortion measures and that our coder results in a better sound quality than baseline transform and parametric coders at 8 and 2 kbit/s. This work constitutes a new step towards a fully object-based coding system, which would represent audio signals as collections of meaningful note-like sound objects

Interpolation-Based Multi-Mode Precoding for MIMO-OFDM Systems with Limited Feedback

Spatial multiplexing with multi-mode precoding provides a means to achieve both high capacity and high reliability in multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. Multi-mode precoding uses linear transmit precoding that adapts the number of spatial multiplexing data streams or modes, according to the transmit channel state information (CSI). As such, it typically requires complete knowledge of the multi-mode precoding matrices for each subcarrier at the transmitter. In practical scenarios where the CSI is acquired at the receiver and fed back to the transmitter through a low-rate feedback link, this requirement may entail a prohibitive feedback overhead. In this paper, we propose to reduce the feedback requirement by combining codebook-based precoder quantization, to efficiently quantize and represent the optimal precoder on each subcarrier, and multi-mode precoder frequency down-sampling and interpolation, to efficiently reconstruct the precoding matrices on all subcarriers based on the feedback of the indexes of the quantized precoders only on a fraction of the subcarriers. To enable this efficient interpolation-based quantized multimode precoding solution, we introduce (1) a novel precoder codebook design that lends itself to precoder interpolation, across subcarriers, followed by mode selection, (2) a new precoder interpolator and, finally, (3) a clustered mode selection approach that significantly reduces the feedback overhead related to the mode information on each subcarrier. Monte-Carlo bit-error rate (BER) performance simulations demonstrate the effectiveness of the proposed quantized multi-mode precoding solution, at reasonable feedback overhead

Dilation dependent matched filtering for SAR signal processing

The relative motion between radar and targets in large time-bandwidth product synthetic aperture radar (SAR) induces serious dilation in the received signal. To process the received signal with serious dilation, a new technique called dilation dependent matched filtering (DDMF) is proposed to combine with the two-dimensional space frequency interpolation wavefront reconstruction (SFIWR) method. The DDMF-SFIWR method can effectively eliminate the impact of dilation when the illuminated area is relatively small, as verified by simulations and acoustic experiments.

AMBIENT NOISE HORIZONTAL-TO-VERTICAL SPECTRAL RATIO FOR ASSESSING SITE EFFECTS IN URBAN ENVIRONMENTS: THE CASE OF THESSALONIKI CITY ( NORTHERN GREECE )

250 ambient noise measurements were performed in a dense grid (about 150mX150m) covering the historical center of the city of Thessaloniki (Northern Greece), that was strongly affected by the 20/6/1978 (M=6.5) damaging earthquake. The data were processed using the method of horizontal- to-vertical (H/V) spectral ratio (Nogoshi and Igarashi, 1971; Nakamura, 1989). In order to evaluate diurnal and seasonal variation (summer - winter) of the ambient noise H/V spectral ratio, systematic measurements were performed in eight sites. The fundamental frequency (fo) and the corresponding H/V amplitude level (Ao) from the ambient noise H/V spectral ratio for each site were calculated. Spatial interpolation of the fundamental frequency (fo) and the corresponding H/V amplitude level (Ao) was attempted between all points and respective contour maps were produced. Diurnal variation of the ambient noise H/V spectral ratio showed that it is preferable to perform measurements during the calm hours of a day, when manmade noise is relatively low. However, no systematic seasonal fluctuation effect on the ambient noise H/V spectral ratio was identified for the city of Thessaloniki. Contour maps of both fundamental frequency (fo) and corresponding H/V amplitude level (Ao) were compared versus the macroseismic data of the 1978 earthquake (Leventakis, 2003), as well as with related geological (IGME, 1978) and geotechnical (Anastasiadis et al., 2001) studies for the same area. Damage distribution due to 20/6/1978 earthquake (Penelis et al., 1985) was also converted to EMS_98 (European Macroseismic Scale, 1998). For seventy buildings, made of reinforced concrete, we have also compared the obtained results with the dynamic amplification of the buildings (Ubuilding) at the fundamental soil frequency (fo). The results encourage the use of ambient noise measurements along with the (H/V) spectral ratio technique as a nonexpensive and fast tool in microzonation studies to be carried out in urban environments.

BROADBAND SIGNAL SIMULATION IN SHALLOW WATER

Today's minimum requirements for ocean acoustic models are to be able to simulate broadband signal transmissions in 2D varying environments with an acceptable computational effort. Standard approaches comprise ray, normal mode and parabolic equation techniques. In this paper we compare the performance of four broadband models [Formula: see text] on a set of shallow-water test environments with propagation out to 10 km and a maximum signal bandwidth of 10–1000 Hz. It is shown that a computationally efficient modal approach as implemented in the [Formula: see text] model is much faster than standard, less optimized models such as [Formula: see text] and [Formula: see text]. However, the handling of range dependency in the adiabatic approximation is not always sufficiently accurate, and it is suggested that a mode coupling approach be adopted in [Formula: see text]. Moreover, the interpolation of modal properties in range could lead to a further significant speed-up of mode calculations in range-dependent environments. It is concluded that coupled modes with wavenumber interpolation in both frequency and range remain the most promising wave modeling approach for broadband signal simulations in range-dependent shallow water environments. At higher frequencies (&gt; 1 kHz) there is currently no alternative to rays as a practical signal simulation tool.

A new algorithm for the estimation of the frequency of a complex exponential in additive Gaussian noise

The letter presents a new algorithm for the precise estimation of the frequency of a complex exponential signal in additive, complex, white Gaussian noise. The discrete Fourier transform (DFT)-based algorithm performs a frequency interpolation on the results of an N point complex fast Fourier transform. For large N and large signal to noise ratio, the frequency estimation error variance obtained is 0.063 dB above the Cramer-Rao bound. The algorithm has low computational complexity and is well suited for real time digital signal processing applications, including communications, radar and sonar.

Concatenative text-to-speech synthesis based on waveform interpolation (a time frequency approach)

The time domain pitch synchronous overlap and add (TD-PSOLA) is the technique most used in comercial concatenative text-to-speech (TTS) synthesis systems. However, it is well known that TD-PSOLA presents several drawbacks. In order to overcome some drawbacks of the TD-PSOLA, this work presents a method based on time frequency interpolation (TFI) [Yair Shoham]. The method introduced here is a pitch-synchronous time-frequency approach of the waveform interpolation technique (WI) [Bastian Kleijn]. The goal of this work is to show that the TFI technique presents some important advantages to concatenative TTS synthesis. It allows pitch scale modification (PSM) independent of time scale modification (TSM) in a quite straightforward manner, and with high quality. TSM and PSM can be done in a continuous way, without any limitation of pitch period resolution. Moreover, the TFI technique allows simple, flexible, and efficient procedures to smooth diphone (or any other kind of unit) boundaries. The proposed system was evaluated using diphones and prosodies generated by the Festival system [Alan Black, Paul Taylor]. Subjective tests were performed, between the proposed TFI system and the standard TD-PSOLA system, highlighting the superior quality of the proposed system in comparison with TD-PSOLA.

Generating Consistent Motion Transition via Decoupled Framespace Interpolation

The framespace interpolation algorithm abstracts motion sequences as 1D signals, and interpolates between them to create higher dimension signals, with weights drawn from a user specified curve in a bounded region. We reformulate the algorithm to achieve motion‐state based transition via dynamic warping of framespaces and automatic transition timing via framespace frequency interpolation. Basis motions displaying diverse coordination configurations between upper and lower body‐halves, cannot be consistently corresponded at a macro level. We address this problem here, through decoupled blending of these halves to achieve true consistency, and eliminate accumulated phase differences via cosine phase warp functions. This generalization enables interpolation of motions with diverse coordinations between the upper and lower bodies.

Parametric interpolation of the moment matrix in surface integral equation formulation

In the analysis of electromagnetic scattering and radiation from objects of arbitrary shape using the method of moments (MoM), it is desirable to fill the impedance (or moment) matrix efficiently so that larger size problems can be solved. This article describes a general MoM technique in which the matrix is filled by spatial interpolation with respect to a parametrized electrical separation between source and test elements. The parametrization is accomplished such that the same algorithm also provides frequency interpolation, thus facilitating efficient computations over a wide frequency band. The spatial interpolation method is illustrated by application to the analysis of radiation from tunable microstrip patch antennas over multiple frequency bands. By specializing the interpolation scheme to a surface integral equation formulation that employs rooftop basis functions on a grid of rectangular cells, it is shown that the interpolation method results in considerable reduction of the storage and CPU time requirements. ©1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 474–489, 1999.