Fast Iterative-Interpolated DFT Phasor Estimator Considering Out-of-band Interference

For interpolated discrete Fourier transform (IpDFT)-based phasor estimators, the out-of-band interference (OOBI) test is among the most challenging ones. The typical iterative-interpolated DFT (i-IpDFT) phasor estimator utilizes a two-step iterative framework to eliminate the effects of the negative frequency and OOBI. However, the speed of estimation is limited by the adopted frequency estimator and the redundant iterations. To this end, this article proposes a fast i-IpDFT (FiIpDFT) method for the phasor estimation of an OOBI contaminated signal, which utilizes the three-point IpDFT (I3pDFT) technique. The proposed method first applies a noniterative frequency, amplitude, and phase estimator to eliminate the negative frequency interference. Then, a straightforward formula and two-stop criterion are introduced to reduce the computational burden of the OOBI elimination process. The accuracy and effectiveness of the proposed FiIpDFT method are validated by simulations. These are designed, under steady and dynamic conditions, according to the requirements of the Standard IEC/IEEE 60255-118-1

Pulsar timing analysis in the presence of correlated noise

Pulsar timing observations are usually analysed with least-square-fitting procedures under the assumption that the timing residuals are uncorrelated (statistically "white"). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.Comment: Accepted by MNRA

Audio Analysis/synthesis System

A method and apparatus for the automatic analysis, synthesis and modification of audio signals, based on an overlap-add sinusoidal model, is disclosed. Automatic analysis of amplitude, frequency and phase parameters of the model is achieved using an analysis-by-synthesis procedure which incorporates successive approximation, yielding synthetic waveforms which are very good approximations to the original waveforms and are perceptually identical to the original sounds. A generalized overlap-add sinusoidal model is introduced which can modify audio signals without objectionable artifacts. In addition, a new approach to pitch-scale modification allows for the use of arbitrary spectral envelope estimates and addresses the problems of high-frequency loss and noise amplification encountered with prior art methods. The overlap-add synthesis method provides the ability to synthesize sounds with computational efficiency rivaling that of synthesis using the discrete short-time Fourier transform (DSTFT) while eliminating the modification artifacts associated with that method.Georgia Tech Research Corporatio

Stepwise Iterative Fourier Transform: The SIFT

A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study