Velocity filters for multiple interference attenuation ingeophysical array data

The problem of velocity filtering a record of seismic data with the objective of extracting a desired signal by attenuating the coherent interferences traveling at different velocities is considered. A two-dimensional (N-input (N-M+1)-output) processing scheme is used where the (N-M+1) output traces are generated from the N-input traces by multichannel processing of overlapping subsets of M-input races. Each output is generated by using a vector of multichannel arrays filters designed to attenuate multiple coherent interference and random noise. The two-dimensional frequency-wavenumber expression corresponding to the proposed multiple-input-multiple-output processing scheme is derived so that it can be implemented using the two-dimensional fast Fourier transform. Two illustrative examples are included     

Systolic arrays for the discrete Hartley transform

Recently, R.N. Bracewell (1983) introduced the discrete Hartley transform (DHT) as an alternative to the discrete Fourier transform (DFT). Two linear systolic array models for the (DHT) are derived. One model requires O(2N-1) in the computational phase and O(N) in the preloading phase. The other model requires O(2N-1) in the computational phase and O(N) in the output phase. A square systolic array for two-dimensional DHT is also constructed by combining the individual advantages of each model. The CORDIC algorithm is proposed as an alternative to conventional multipliers. To speed up the systolic array, two-level pipelining with CORDIC is also possible     

Simplified fast least-squares algorithms for speech predictors

The letter deals with the development of a simplified fast least-squares algorithm which is free of roundoff error accumulation. The simplified algorithm requires 9N MADPR (multiplications and divisions per recursion) rather than 10N MADPR as in the fast least squares or fast Kalman (FLS) case where N is the order of predictor. The superiority of SFLS over FLS and LMS approaches is illustrated by prediction gain performance curves for various speech signals     

Fast cosine transform of Toeplitz matrices, algorithm andapplications

A fast algorithm for the discrete cosine transform (DCT) of a Toeplitz matrix of order N is derived. Only O(N log N)+O(M) time is needed for the computation of M elements. The storage requirement is O(N). The method carries over to other transforms (DFT, DST) and to Hankel or circulant matrices. Some applications of the algorithm are discussed     

Quadtree-structured recursive plane decomposition coding of images

The approximation of two-dimensional highly correlated grey value functions can be performed using a linear model of the type f( x, y)=a+bx+cy. The set of plane parameters (PPs) [a, b, c] can be determined in the least squares sense for a block of size N×N pixels, for example. Starting with a block size of 2×2 pixels, it is shown that the PPs obey a recursive law such that the PPs of a 2N×2N block can be computed recursively when only the PPs of the four adjacent subblocks of size N×N in the lower decomposition level are known. This concept of recursive plane decomposition (RPD) is embedded in a quadtree data structure to obtain a new variable block size image coding algorithm that offers a high performance at a low computational cost. Extensive comparisons to other state-of-the-art image coding algorithms are reported     

Zero-crossings of a wavelet transform

The completeness, stability, and application to pattern recognition of a multiscale representation based on zero-crossings is discussed. An alternative projection algorithm is described that reconstructs a signal from a zero-crossing representation, which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero-crossings. The reconstruction algorithm has a fast convergence and each iteration requires O( N log² (N)) computation for a signal of N samples. The zero-crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems. As an example, the implementation and results of a coarse-to-fine stereo-matching algorithm are described     

Analysis of modified SMI method for adaptive array weight control

The authors characterize the performance of the diagonally loaded sample matrix inverse (SMI) algorithm versus the number K of snapshots used in the covariance matrix estimate by providing O(1/K) statistics (bias and variance) of the array weights, output powers, and output power ratios such as signal to interference noise ratio (SINR) and INR. The approach accommodates wideband signals. Monte Carlo simulations verify the theoretical analysis     

In the optimum design of the block adaptive FIR digital filter

A general optimum block adaptive (GOBA) algorithm for adaptive FIR (finite impulse response) filtering is presented. In this algorithm, the correction terms for the filter coefficients in each block, instead of the convergence factors, are optimized in a least squares sense. There are no constraints on the block length L and the filter tap number N. It is shown that the GOBA algorithm is reduced to the normalized LMS algorithm when L⩾N. The convergence of the GOBA algorithm can be assured if the correlation matrix of the input signal is positive definite. Computer simulations based on an efficient computing procedure confirm that the GOBA algorithm achieves faster convergence with slightly degraded convergence accuracy in stationary environments and better weight tracking capability in nonstationary environments as compared to existing block adaptive algorithms with no constraints on L and N     

Queueing in high-performance packet switching

The authors study the performance of four different approaches for providing the queuing necessary to smooth fluctuations in packet arrivals to a high-performance packet switch. They are (1) input queuing, where a separate buffer is provided at each input to the switch; (2) input smoothing, where a frame of b packets is stored at each of the input line to the switch and simultaneously launched into a switch fabric of size Nb×Nb; (3) output queuing, where packets are queued in a separate first-in first-out (FIFO) buffer located at each output of the switch; and (4) completely shared buffering, where all queuing is done at the outputs and all buffers are completely shared among all the output lines. Input queues saturate at an offered load that depends on the service policy and the number of inputs N, but is approximately 0.586 with FIFO buffers when N is large. Output queuing and completely shared buffering both achieve the optimal throughput-delay performance for any packet switch. However, compared to output queuing, completely shared buffering requires less buffer memory at the expense of an increase in switch fabric size     

Performance analysis of nonblocking packet switch with input andoutput buffers

The performance of nonblocking packet switches such as the knockout switch and Batcher banyan switch for high-speed communication networks can be improved as the switching capacity L per output increases; the switching capacity per output refers to the maximum number of packets transferred to an output during a slot. The N×N switch with L=N was shown to attain the best possible performance by M.J. Karol et al. (1987). Here a N×N nonblocking packet switch with input and output buffers is analyzed for an arbitrary number of L such that 1⩽L⩽N. The maximum throughput and packet loss probability at input are obtained when N=∞     

Optimization of signal sets for partial-response channels. I.Numerical techniques

Given a linear, time-invariant, discrete-time channel, the problem of constructing N input signals of finite length K that maximize minimum l₂ distance between pairs of outputs is considered. Two constraints on the input signals are considered: a power constraint on each of the N inputs (hard constraint) and an average power constraint over the entire set of inputs (soft constraint). The hard constraint, problem is equivalent to packing N points in an ellipsoid in min(K,N-1) dimensions to maximize the minimum Euclidean distance between pairs of points. Gradient-based numerical algorithms and a constructive technique based on dense lattices are used to find locally optimal solutions to the preceding signal design problems. Two numerical examples are shown for which the average spectrum of an optimized signal set resembles the water pouring spectrum that achieves Shannon capacity, assuming additive white Gaussian noise     

Upper bounds on capacity for a constrained Gaussian channel

A low-pass and a bandpass additive white Gaussian noise channel with a peak-power constraint imposed on otherwise arbitrary input signals are considered. Upper bounds on the capacity of such channels are derived. They are strictly less than the capacity of the channel when the peak-power constrain is removed and replaced by the average-power constraint, for which the Gaussian inputs are optimum. This provides the answer to an often-posed question: peak-power limiting in the case of bandlimited channels does reduce capacity, whereas in infinite bandwidth channels it does not, as is well known. For an ideal low-pass filter of bandwidth B, the upper bound is Blog 0.934P/(N₀B) for P/( N₀B)≫1, where P is the peak power of the input signal and N₀/2 is the double-sided power spectral density of the additive white Gaussian noise     

A generalized recursive algorithm for wave-scattering solutions intwo dimensions

A generalized recursive algorithm valid for both the E _z and H_z wave scattering of densely packed scatterers in two dimensions is derived. This is unlike previously derived recursive algorithms which have been found to be valid only for E_z polarized waves. In this generalized recursive algorithm, a scatterer is first divided into N subscatterers. The n-subscatterer solution is then used to solve the (n+n')-subscatterer solution. The computational complexity of such an algorithm is found to be of O (N²) in two dimensions while providing a solution valid for all angles of incidence. This is better than the method of moments with Gaussian elimination, which has an O(N³) complexity     

Error performance of a digitally processed binary ESK frequencyhopping receiver in the presence of large Doppler

Analysis is made of the effects of Doppler on the error rate performance of a low data rate binary FSK frequency hopping receiver, employing a discrete Fourier transform (DFT) technique for baseband detection. Bit detection decision is made by locating the maximum of the DFT outputs which, in the frequency domain, are assumed to be separated by 1/T where T is the bit period. Both the worst case and average error performances are obtained and presented as a function of E_b/N₀ for various values of M where E_b/N₀ is the signal bit energy-to-noise density ratio and M is the degree of freedom associated with the Doppler uncertainty window. The E _b/N₀ degradation as a function of M is also presented     

An algorithm for determining if a rate (n-1)/npunctured convolutional encoder is catastrophic

The algorithm determines whether or not the punctured state diagram contains a zero-weight cycle. The punctured encoder is assumed to be obtained from a rate 1/b, b⩽n, antipodal encoder of a given constraint length. The algorithm is much simpler to implement in software than the previously known method of calculating the GCD of the determinants of the n distinct (n-1)×(n-1) submatrices of the generator matrix. The computational complexity of the algorithm is no worse than the computational complexity of the GCD method for relatively short constraint lengths, that is, the constraint lengths for which the Viterbi algorithm is implemented     

Design of bipolar imaging devices (BASIS): analysis of random noise

A design methodology for a bipolar imaging device, the base-stored image sensor (BASIS), has been established by theoretical analysis and experimental verification for random noise. The random noise in BASIS is dominated by the shot noise in readout and transient reset operation. The theoretical analysis has been carried out by introducing the probability density functions for these operations. The readout noise depends on the base-to-collector junction capacitance C_bc , the emitter common current gain h_FE, the storage capacitor C_T, and the emitter voltage V _E. The reset noise has been confirmed to be given by thermal noise. The theoretical results coincide well with the experimental results obtained by TEG devices. An expression for the S/N ratio has been derived theoretically. It is found that h_FE should be made as large as possible and ( C_bc+C_be) as small as possible to improve the S/N ratio for random noise, where C _be is the base-to-emitter junction capacitance     

On the effect of gap width on the admittance of solid circularcylindrical dipoles

A center-fed, solid, circular cylindrical dipole of radius a with feed gap of width 2d radiating in a circular waveguide of radius b terminated in infinite ground planes is rigorously analyzed by applying both the conservation-of-complex-power technique and the multiple-reflections technique. The analysis begins by studying the dependence of the dipole admittance on its feed gap width and on its length, 2l, as well as on b, with ka (k=2π/λ is the number) as a parameter. From the decreasing amplitudes of the almost periodic oscillations of these input admittances as b/λ is increased, the input admittances of dipoles radiating in free space (b→∞) are estimated using a variable-bound approach. The effect of gap width (d/a⩽5) for different lengths of dipoles (0.2⩽2l/λ⩽1) in free space and for different thicknesses (ka⩽0.2) is then established. The feed gap dependence for a half-wave dipole is also examined in detail for d /a⩽10 and ka⩽0.14     

Complete classification of roots to one-dimensional median andrank-order filters

The set of roots to the one-dimensional median filter is completely determined. Let 2N+1 be the filter window width. It has been shown that if a root contains a monotone segment of length N+1, then it must be locally monotone N+2. For roots with no monotone segment of length N+1, it is proved that the set of such roots is finite, and that each such root is periodic. The methods used are constructive, so given N, one can list all possible roots of this type. The results developed for the median filter also apply to rank-order filters     

On the existence of optimum cyclic burst correcting codes over GF(q)

A cyclic b-burst correcting code over GF(q) of redundancy r and length n=(q^r-b+1-1)/(q-1) is said to be optimum. It is proved that a necessary condition for the existence of such a code is the existence of a square-free polynomial in GF(q)[x] of degree b-1 which is not divisible by x such that its period and the degrees of its irreducible factors are relatively prime to q-1. Moreover, if such a polynomial exists, then there are an infinite number of optimum cyclic b-burst correcting codes over GF(q)     

Design and characterization of optimal FIR filters with arbitraryphase

An algorithm for designing a Chebyshev optimal FIR filter that approximates an arbitrary complex-valued frequency response is presented. This algorithm computes the optimal filter by solving the dual to the filter design problem. It is guaranteed to converge theoretically and requires O(N²) computations per iteration for a filter of length N. For the first time, properties of the optimal filter are derived, and the case where the desired filter has arbitrary constant group delay is studied in detail