Modelling Non-Homogeneous Poisson Processes with Almost Periodic Intensity Functions

Efforts to develop algorithms that can identify the modulation type of a signal and determine whether that signal varies continuously or takes on a finite number of discrete states are detailed. The approach used for determining the modulation type of a signal is to: (1) extract statistics about the time variation of the amplitude, frequency, and phase of a signal, (2) combine these statistics into interpretable features, and (3) associate these features with a modulation type using a suitably defined modulation space and metric. The algorithms were validated by performing Monte Carlo simulations to determine the accuracy of the estimators. The amplitude, phase, and frequency estimators were evaluated by calculating the mean and the standard deviations of the error distributions. The accuracy of the amplitude estimator was virtually unaffected by the sampling rate. However, the noise added to the signal did have an effect on the estimator's accuracy. The frequency estimator was affected by both the sampling rate and the amount of additive noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper discusses a least-squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series. It is shown that the usual asymptotics on estimation of frequency, amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective. Computational issues are discussed and some illustrations are provided. Bolt & Brillinger (1979) make use of these asymptotic results.

Preface. 1 Spread spectrum signals and systems. 1.1 Basic definition. 1.2 Historical sketch. 2 Classical reception problems and signal design. 2.1 Gaussian channel, general reception problem and optimal decision rules. 2.2 Binary data transmission (deterministic signals). 2.3 M-ary data transmission: deterministic signals. 2.4 Complex envelope of a bandpass signal. 2.5 M-ary data transmission: noncoherent signals. 2.6 Trade-off between orthogonal-coding gain and bandwidth. 2.7 Examples of orthogonal signal sets. 2.8 Signal parameter estimation. 2.9 Amplitude estimation. 2.10 Phase estimation. 2.11 Autocorrelation function and matched filter response. 2.12 Estimation of the bandpass signal time delay. 2.13 Estimation of carrier frequency. 2.14 Simultaneous estimation of time delay and frequency. 2.15 Signal resolution. 2.16 Summary. Problems. 3 Merits of spread spectrum. 3.1 Jamming immunity. 3.2 Low probability of detection. 3.3 Signal structure secrecy. 3.4 Electromagnetic compatibility. 3.5 Propagation effects in wireless systems. 3.6 Diversity. 3.7 Multipath diversity and RAKE receiver. Problems. 4 Multiuser environment: code division multiple access. 4.1 Multiuser systems and the multiple access problem. 4.2 Frequency division multiple access. 4.3 Time division multiple access. 4.4 Synchronous code division multiple access. 4.5 Asynchronous CDMA. 4.6 Asynchronous CDMA in the cellular networks. Problems. 5 Discrete spread spectrum signals. 5.1 Spread spectrum modulation. 5.2 General model and categorization of discrete signals. 5.3 Correlation functions of APSK signals. 5.4 Calculating correlation functions of code sequences. 5.5 Correlation functions of FSK signals. 5.6 Processing gain of discrete signals. Problems. 6 Spread spectrum signals for time measurement, synchronization and time-resolution. 6.1 Demands on ACF: revisited. 6.2 Signals with continuous frequency modulation. 6.3 Criterion of good aperiodic ACF of APSK signals. 6.4 Optimization of aperiodic PSK signals. 6.5 Perfect periodic ACF: minimax binary sequences. 6.6 Initial knowledge on finite fields and linear sequences. 6.7 Periodic ACF of m-sequences. 6.8 More about finite fields. 6.9 Legendre sequences. 6.10 Binary codes with good aperiodic ACF: revisited. 6.11 Sequences with perfect periodic ACF. 6.12 Suppression of sidelobes along the delay axis. 6.13 FSK signals with optimal aperiodic ACF. Problems. 7 Spread spectrum signature ensembles for CDMA applications. 7.1 Data transmission via spread spectrum. 7.2 Designing signature ensembles for synchronous DS CDMA. 7.3 Approaches to designing signature ensembles for asynchronous DS CDMA. 7.4 Time-offset signatures for asynchronous CDMA. 7.5 Examples of minimax signature ensembles. Problems. 8 DS spread spectrum signal acquisition and tracking. 8.1 Acquisition and tracking procedures. 8.2 Serial search. 8.3 Acquisition acceleration techniques. 8.4 Code tracking. Problems. 9 Channel coding in spread spectrum systems. 9.1 Preliminary notes and terminology. 9.2 Error-detecting block codes. 9.3 Convolutional codes. 9.4 Turbo codes. 9.5 Channel interleaving. Problems. 10 Some advancements in spread spectrum systems development. 10.1 Multiuser reception and suppressing MAI. 10.2 Multicarrier modulation and OFDM. 10.3 Transmit diversity and space-time coding in CDMA systems. Problems. 11 Examples of operational wireless spread spectrum systems. 11.1 Preliminary remarks. 11.2 Global positioning system. 11.3 Air interfaces cdmaOne (IS-95) and cdma2000. 11.4 Air interface UMTS. References. Index.

A parameter (i.e. frequency, amplitude and phase) estimation method of acoustic signals is proposed. The frequency estimation of the proposed method is basically based on the linear prediction (LP) model. The ordinary LP model assumes that the number of frequency components in the signal is given. The proposed method improves the ordinary LP model so as to be applicable for the case where the number of the frequency components is unknown. The amplitude and phase estimation of the proposed method is based on the modified least square error method. Simulation results are provided to confirm the effectiveness of the proposed method.

Electrocochleography (ECochG) is increasingly used to monitor the inner ear function of cochlear implant (CI) patients during surgery. Current ECochG-based trauma detection shows low sensitivity and specificity and depends on visual analysis by experts. Trauma detection could be improved by including electric impedance data recorded simultaneously with the ECochG. However, combined recordings are rarely used because the impedance measurements produce artifacts in the ECochG. In this study, we propose a framework for automated real-time analysis of intraoperative ECochG signals using Autonomous Linear State-Space Models (ALSSMs). We developed ALSSM based algorithms for noise reduction, artifact removal, and feature extraction in ECochG. Feature extraction includes local amplitude and phase estimations and a confidence metric over the presence of a physiological response in a recording. We tested the algorithms in a controlled sensitivity analysis using simulations and validated them with real patient data recorded during surgeries. The results from simulation data show that the ALSSM method provides improved accuracy in the amplitude estimation together with a more robust confidence metric of ECochG signals compared to the state-of-the-art methods based on the fast Fourier transform (FFT). Tests with patient data showed promising clinical applicability and consistency with the findings from the simulations. We showed that ALSSMs are a valid tool for real-time analysis of ECochG recordings. Removal of artifacts using ALSSMs enables simultaneous recording of ECochG and impedance data. The proposed feature extraction method provides the means to automate the assessment of ECochG. Further validation of the algorithms in clinical data is needed.

We discuss in this paper a non-homogeneous Poisson process Π∘A driven by an almost periodic intensity function. We give the stationary version Π∘A * and the Palm version Π∘A 0 corresponding to Π∘A *. Let (T i ,i∈ℕ) be the inter-point distance sequence in Π∘A and (T 0 ,i∈ℕ) in Π∘A 0. We prove that forj→∞, the sequence (T i+j,i∈ℕ) converges in distribution to (T i 0 ,i∈ℕ). If the intensity function is periodic then the convergence is in variation.

The main topic of this paper is the nonparametric estimation of complex (both amplitude and phase) spectra from gapped data, as well as the restoration of such data. The focus is on the extension of the APES (amplitude and phase estimation) approach to data sequences with gaps. APES, which is one of the most successful existing nonparametric approaches to the spectral analysis of full data sequences, uses a bank of narrowband adaptive (both frequency and data dependent) filters to estimate the spectrum. A recent interpretation of this approach showed that the filterbank used by APES and the resulting spectrum minimize a least-squares (LS) fitting criterion between the filtered sequence and its spectral decomposition. The extended approach, which is called GAPES for somewhat obvious reasons, capitalizes on the aforementioned interpretation: it minimizes the APES-LS fitting criterion with respect to the missing data as well. This should be a sensible thing to do whenever the full data sequence is stationary, and hence the missing data have the same spectral content as the available data. We use both simulated and real data examples to show that GAPES estimated spectra and interpolated data sequences have excellent accuracy. We also show the performance gain achieved by GAPES over two of the most commonly used approaches for gapped-data spectral analysis, viz., the periodogram and the parametric CLEAN method.

In this Letter, the maximum likelihood (ML) estimator for the parameters of a real sinusoid in additive white Gaussian noise using irregularly-spaced samples is derived. The ML frequency estimate is first determined by a one-dimensional search, from which optimum amplitude and phase estimates are then computed. It is shown that the estimation performance of the ML method can attain Cramer-Rao lower bound when the signal-to-noise ratio is sufficiently large.

An adaptive array algorithm is proposed to mit- igate against the presence of co-channel interference or hos- tile jammers for a GPS receiver. The unknown time and frequency offset estimation for the receiver, employs Markov Chain Monte Carlo (MCMC) integration, utilizing a novel, multi- dimensional, Bayesian, global optimization strategy for initializ- ing a Metropolis-Hastings proposal distribution. The technique enables the design of a high performance multi-user receiver, capable of overcoming the near-far problem, mitigates multipath and interference and provides significantly improved time and frequency estimation performance over standard matched filter algorithm approaches.

We present an algorithm for nonparametric complex spectral analysis of gapped data via an adaptive finite impulse response (FIR) filtering approach, referred to as the gapped-data amplitude and phase estimation (GAPES) algorithm. The incomplete data sequence may contain gaps of various sizes. The GAPES algorithm iterates the following two steps: (1) estimating the adaptive FIR filter and the corresponding complex spectrum via amplitude and phase estimation (APES), a nonparametric adaptive FIR filtering approach, and (2) filling in the gaps via a least-squares APES fitting criterion. The initial condition for the iteration is obtained from the available data segments via APES. Numerical results are presented to demonstrate the effectiveness of the proposed GAPES algorithm.

Adaptive optics systems are commonly used in many optical structures to reduce perturbations and to increase the system performance. The problem in such systems is undesirable vibrations due to some effects as shaking of the whole structure or the tracking process. This paper presents a frequency, amplitude and phase estimation method of a multifrequency signal that can be used to reject these vibrations in an adaptive method. The estimation method is based on using the FFT procedure. The undesirable signals are usually exponentially damped harmonic oscillations. The estimation error depends on several parameters and consists of a systematic component and a random component. The systematic error depends on the signal phase, the number of samples N in a measurement window, the value of CiR (number of signal periods in a measurement window), the THD value and the time window order H . The random error depends mainly on the variance of noise and the SNR value. This paper shows research on the sinusoidal signal phase and the estimation of exponentially damped sinusoids parameters. The shape of errors signals is periodical and it is associated with the signal period and with the sliding measurement window. For CiR =1.6 and the damping ratio 0.1% the error was in the order of 10 -5 Hz/Hz, 10 -4 V/V and 10 -4 rad for the frequency, the amplitude and the phase estimation respectively. The information provided in this paper can be used to determine the approximate level of the efficiency of the vibrations elimination process before starting it.

Due to its simplicity and accuracy, quadratic peak interpolation in a zero-padded fast Fourier transform (FFT) has been widely used for sinusoidal parameter estimation in audio applications. We propose, as its natural extension, a method to estimate the first order amplitude and frequency modulation rates of time-varying sinusoidal components, as well as to correct biases in conventional amplitude, frequency and phase estimates. We derive exact formulas for Gaussian windows and obtain approximate formulas for often-used windows by introducing a simple window adaptation scheme. Experimental results show the average estimation biases of the AM and FM rates with a 30 ms Hann window are below 1% for typical AM/FM rates in speech.

Phase estimation plays an important role in various signal processing areas like Radar, Sonar, power systems, speech analysis, communications and many others. The phase of the analytic form of the non stationary signals can be used to find instantaneous frequency. This paper addresses the problem of simultaneous phase and instantaneous frequency estimation from polynomial phase signals embedded in Gaussian noise. Here we have introduced the modified signal tracking approach which is then realized using unscented Kalman filter. The state space model is derived using Taylor series expansion of the phase of polynomial phase signal as process model while Polar to Cartesian conversion as measurement model. Proposed method, compared with state-of-the-art, performs better for signals with higher order polynomial phase variations at lower Signal-to-Noise-Ratio (0-5dB). We also present the simulation results for phase estimation.

An algorithm for harmonic decomposition of time-variant signals is derived from a least squares harmonic (LSH) technique. The estimates of harmonic amplitudes and phases are formulated as the solution of a set of linear equations which minimizing mean square error; the signal frequency is modeled by a linear or quadratic polynomial and obtained via a local search over polynomial coefficients. An initial estimate of signal frequency is necessary to reduce computation time. This method is capable of producing accurate and robust harmonic estimation in low SNR situations. We show applicability to high accuracy speech pitch and heart sound beat epoch estimation.

The paper deals with the estimation of amplitude and phase of an analogue multi-harmonic band-limited signal from irregularly spaced sampling values. To this end, assuming the signal fundamental frequency is known in advance (i.e., estimated at an independent stage), we propose a complexity-reduced algorithm for signal reconstruction in time domain. The proposed method of processing can be used for precise rms measurements (for power and energy) of a periodic signal based on the presented signal reconstruction. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.