Unsupervised estimation of signals with intersymbol interference (Corresp.)

A decision-directed unsupervised estimation algorithm is used in a receiver that processes signals with unknown intersymbol interference. The estimator utilizes the statistical structure of this dependent sample problem to reduce the computational complexity. Asymptotic and experimental dynamic probability of error results are presented.     

Recursive parameter estimation for noisy autoregressive signals (Corresp.)

The problem of recursively estimating the unknown parameters of a scalar autoregressive (AR) signal observed in additive white noise, including signal power and noise variance, is considered. A state-space model in a canonical but noninnovations form is used to represent the noisy AR signal. An algorithm based on a system identification/parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation. Two simulation examples illustrate the effectiveness of the proposed algorithm.     

On optimal linear estimation of signals with general spectral distribution (Corresp.)

It is standard practice to assume that second-order stationary signal and noise processes involved in a linear estimation procedure have spectral densities. A heuristic justification may be based on the reasoning that the part of the signal having singular spectral distribution can be precisely determined, and the part of the noise having singular spectral distribution can be completely eliminated. Rigorous phrasing and proof of this claim are given here for the most general case, i.e., where the singular parts of the spectral distributions may contain continuous components, in which situation the intuitive picture is obscure. The discussion includes both discrete-time and continuous-time processes, and the multivariable case is also treated.     

Detection of quantum signals of random phase in thermal noise (Corresp.)

When the phase of the transmittance between a unimodal transmitter and a unimodal receiver is uniformly distributed over(0,2pi), the density operator of the received signal field commutes with the photon number operator, and the optimum detector of the signal counts photons. A simple formula is given for the probability generating function of the number of photons in terms of the quasi-probability distribution of the transmitted signal. It is used to determine the average error probability of an on-off binary communication system transmitting two-photon coherent-state signals, received in the presence of thermal noise.     

Resolution of overlapping random signals (Corresp.)

This correspondence is concerned with the estimation and resolution of overlapping random signals in additive noise. Two resolution schemes are presented; one is optimal and the other has computational advantages. It is shown that the overlapping signals are not resolvable if the eigenfunctions constitute a complete basis.     

Reconstruction of finite duration signals (Corresp.)

The problem of reconstructing a finite-duration finite-energy signal that has been band limited and sampled is considered. An interpolation formula is derived that, in principle, permits perfect signal reconstruction in the noiseless case provided only that the sampling frequency exceeds the cutoff frequency of the band-limiting filter. The degradation introduced by measurement noise on the samples is evaluated.     

Combined quantization-detection of uncertain signals (Corresp.)

Combined quantization-detection of uncertain signals is considered. The distribution of the uncertain signal is not completely known, although it is known to belong to a finite set of possibilities. A simultaneous quantization-detection system consisting of a detector and a bank of quantizers is suggested. An example is presented for illustration.     

Variance estimation and adaptive quantization (Corresp.)

The relationship between variance estimation and adaptive quantization is investigated for memoryless Laplacian and Gaussian sources. Comparison of block average, exponential average, and maximum likelihood estimators in an adaptive quantization scheme indicates that estimator precision (variance) is more important than accuracy (bias) in minimizing distortion. Further, the block average and exponential average estimators are inconsistent when used in backward adaptive quantization.     

Proof of Rife and Boorstyn's hypothesis on estimation of parameters of multitone signals (Corresp.)

It is shown that the Fisher information matrix appropriate to estimation of the parameters of a multitone signal by use of equally spaced samples is singular only if duplicates modulo2pi /Texist among the tone frequencies. This confirms a hypothesis of Rife and Boorstyn.     

Robust detection to stochastic signals (Corresp.)

In this correspondence we evaluate both the large and small sample performance of a limiter-quadratic detector (LQD) for the detection of a Gaussian signal in non-Gaussian noise. The LQD is shown to be robust for small as well as large sample sizes.     

Sampling theorem for finite-energy signals (Corresp.)

It is shown that the Shannon sampling expansion for finite-energy bandlimited signals is a special case of the Parseval relation for complex Fourier series.     

On the detectability of weak signals (Corresp.)

Approximate performance results are obtained for optimal detection of weak discrete time signals. The analysis parallels the "locally optimum" approach for detector design and is based on a small-signal Taylor series approximation to the Chernoff error probability bounds.     

Conversion of sequency-limited signals into frequency-limited signals and vice versa (Corresp.)

Sequency-limited signals, consisting of a superposition of Walsh functions, and frequency-limited signals, consisting of a superposition of sine-cosine functions, can readily be converted from one form to the other without wasting either frequency or sequency bandwidth.     

Observation delays in sequential estimation (Corresp.)

In this correspondence the problem of sequential estimation is considered when the observation delays are, in general, costly. General theorems determining the "optimal" stopping time in this case are stated, and specific cases are worked out.     

On decision-directed estimation and stochastic approximation (Corresp.)

A decision-directed scheme for estimating the mean is expressed as a stochastic approximation algorithm. The algorithm is shown to converge, but not to the true value, by means of the theory of stochastic approximation. A modification of the algorithm that converges to the true value is presented.     

Detection and diagnosis of abrupt changes in modal characteristics of nonstationary digital signals (Corresp.)

New "instrumental" tests for detecting and diagnosing changes in the poles of a signal having unknown time-varying zeros are proposed. Numerical results for nonstationary scalar signals are given. The extension of these tests to the vector case may be used for vibration monitoring.