Showing papers on "Multidimensional signal processing published in 1987"

Discrete radon transform

Abstract: This paper describes the discrete Radon transform (DRT) and the exact inversion algorithm for it. Similar to the discrete Fourier transform (DFT), the DRT is defined for periodic vector-sequences and studied as a transform in its own right. Casting the forward transform as a matrix-vector multiplication, the key observation is that the matrix-although very large-has a block-circulant structure. This observation allows construction of fast direct and inverse transforms. Moreover, we show that the DRT can be used to compute various generalizations of the classical Radon transform (RT) and, in particular, the generalization where straight lines are replaced by curves and weight functions are introduced into the integrals along these curves. In fact, we describe not a single transform, but a class of transforms, representatives of which correspond in one way or another to discrete versions of the RT and its generalizations. An interesting observation is that the exact inversion algorithm cannot be obtained directly from Radon's inversion formula. Given the fact that the RT has no nontrivial one-dimensional analog, exact invertibility makes the DRT a useful tool geared specifically for multidimensional digital signal processing. Exact invertibility of the DRT, flexibility in its definition, and fast computational algorithm affect present applications and open possibilities for new ones. Some of these applications are discussed in the paper.

Theoretical analysis of the max/Median filter

Abstract: Median filtering has been used successfully for extracting features from noisy one-dimensional signals; however, the extension of the one-dimensional case to higher dimensions has not always yielded satisfactory results. Although noise suppression is obtained, too much signal distortion is introduced and many features of interest are lost. In this paper, we introduce a multidimensional filter based on a combination of one-dimensional median estimates. It is shown that threshold decomposition holds for this class of filters, making the deterministic analysis simpler. Invariant signals to the filter, called root signals, consist of very low resolution features making this filter much more attractive than conventional median filters.

VLSI Architectures for Multidimensional Fourier Transform Processing

Abstract: It is often desirable in modern signal processing applications to perform two-dimensional or three-dimensional Fourier transforms. Until the advent of VLSI it was not possible to think about one chip implementation of such processes. In this paper several methods for implementing the multidimensional Fourier transform together with the VLSI computational model are reviewed and discussed. We show that the lower bound for the computation of the multidimensional transform is O(n2 log2 n). Existing nonoptimal architectures suitable for implementing the 2-D transform, the RAM array transposer, mesh connected systolic array, and the linear systolic matrix vector multiplier are discussed for area time tradeoff. For achieving a higher degree of concurrency we suggest the use of rotators for permutation of data. With ``hybrid designs'' comprised of a rotator and one-dimensional arrays which compute the one-dimensional Fourier transform we propose two methods for implementation of multidimensional Fourier transform. One design uses the perfect shuffle for rotations and achieves an AT2 p of O(n2 log2 n· log2 N). An optimal architecture for calculation of multidimensional Fourier transform is proposed in this paper. It is based on arrays of processors computing one-dimensional Fourier transforms and a rotation network or rotation array. This architecture realizes the AT2 p lower bound for the multidimensional FT processing.

On the performance of signal-subspace processing--Part II: Coherent wide-band systems

Abstract: This is the second part of a study which deals with the performance of multiple-source direction finding via signal-subspace processing [1]. An analytical evaluation of detection (determination of the number of sources) and direction estimation performance is presented for the coherent wide-band signal-subspace processing algorithm [2], which operates on the received array signals of large relative bandwidth. The probabilities of underestimating and overestimating the number of sources are derived, under asymptotic conditions and in the threshold regions, in terms of the choice of a penalty function and signal, noise, and array parameters for the cases of at most two closely spaced sources in spatially white noise. A scalar measure is used for the evaluation of the quality of the estimated signal subspaces. It is shown that the detection and estimation performances of the practical coherent algorithm are close to those of the perfectly coherent processing, and that they are relatively insensitive with respect to a preliminary estimate of the angles used to effect an approximate coherence.

Reconstruction of nonperiodic two-dimensional signals from zero crossings

Abstract: In this correspondence, we present new results on the reconstruction of two-dimensional signals from zero crossing or threshold crossing information. Specifically, we develop new theoretical results which state conditions under which two-dimensional bandlimited signals are uniquely specified to within a scale factor with this information. Unlike previous results in this area, our new results do not constrain the signals to be periodic or bandpass.

Binary tree multiprocessor

Abstract: A binary tree multiprocessing array of plural signal processing elements, and having input/output for the array entirely through a root one of the processing elements, includes in each processing element thereof a hardware, pipelined, floating point, multiply/accumulate processing function for cooperating with a procesing element memory and a processing element input/output processing function to perform signal pattern matching of input digital signal sequences provided to and/or through the root processing element with respect to at least one digital signal sequence pattern stored in the memory.

Resolution of coherent signals using a linear array

Abstract: A high resolution algorithm for resolving closely spaced incident plane waves impinging on a linear array is presented. Unlike many existing "noise eigenvector" based methods, this "signal eigenvector" algorithm is not susceptible to the difficulties arising from coherent signal sources. A complete theoretical development of this algorithm is provided. Its improved performance relative to the spacial smoothed version of MUSIC is illustrated by simulated examples.

Method and apparatus for waveform reconstruction for sampled data system

Abstract: Representations of signal edges of a repetitive signal are sampled without triggering, then sorted out based on frequency and sequence and then superimposed along a common time base of one period in order to reconstruct a signal. In a specific embodiment of a method according to the invention, a string of samples of a repetitive, input signal with high frequency components is captured without triggering with relatively low time resolution to determine an approximate waveform from the low resolution samples, then digital signal processing techniques in the form of a fast Fourier transform are applied to a reconstructed time record of the input signal to obtain an accurate frequency for each signal component, and finally the sampled waveform is reconstructed by overlaying sampled components with reference to a common time or phase reference. The FFT is employed to determine the frequency of each signal component very accurately. Further processing, such as bin interpolation based on a window function, may be employed to improve resolution still further.

Digital signal processing method for real-time processing of narrow band signals

Abstract: A digital signal processing method for real-time processing of narrow band signals to provide for reconstitution of dynamic amplitude and harmonics beyond the passband. The method utilizes a digital microprocessor implementing a digital algorithm upon a digitized sample of the analog signals. After processing digital-to-analog conversion circuitry may be used to reconvert the processed digital signal into a processed analog output signal for further use. The digital processing effectively provides a primary voltage compressor (PVC) function for processing signals in m different frequency sub-bands by gain factors, and a summing function for digitally summing the gain products so realized, to provide a primarily compressed signal. The processing method then further effectively provides a secondary dynamic voltage compressor (SDC) function for processing the PVC signal in within n different frequency sub-bands by digitally multiplying signals with each of such sub-bands by gain factors. The further gain products so realized are digitally summed to provide a processed digital output. An AGC gain calculation is also provided by the digital processor for providing a gain-corrected digital output which may then be supplied to D/A converter circuitry. Both fast and slow gain averaging are utilized in making the gain calculation for gain multiplication within each of m sub-bands of the PVC function. The sub-bands m and n of the PVC and SDC functions may be equal in number and have corresponding frequency domains.

Implementation of digital filtering algorithms using pipelined vector processors

Abstract: The implementation of digital filtering algorithms using pipelined vector processors is investigated. Modeling of vector processors and vectorization methods are explained, and then the performances of several implementation methods are evaluated based on the model. Vector processor implementation of FIR filtering algorithms using the outer product method and the indirect convolution method is evaluated. Recursive and adaptive filtering algorithms, which lead to dependency problems in direct vector processor implementations, are implemented very efficiently using a newly developed vectorization method. The proposed method computes multiple output samples at a time, making the vector length independent of the filter order. Illustrative examples comparing theoretical results with Cray X-MP simulation results are included.

Signal synthesis from pseudo-Wigner distribution and applications

Abstract: This paper is concerned with mixed time-frequency signal representation and processing using pseudo-Wigner distribution (PWD). In this approach, the PWD is modified, and a signal is to be synthesized from the modified PWD. Two algorithms, the "outer-product approximation" (OPA) and the "overlapping method" (OM), based on outer-product formulation are presented. Experimental results include noise smoothing and signal separation in the time-frequency domain.

Transforms for Engineers: A Guide to Signal Processing

Abstract: Abbreviations and symbols Digital signal processing Orthogonality and domain transformation Matrices and other essential mathematics Fast Fourier transformations Other fast transformations Implementation Speech processing and communications Sonar, seismology, and radar Biomedicine Image processing Selected additional references.

Architectures for multiplierless fast Fourier transform hardware implementation in VLSI

Abstract: This paper presents a novel processor for the implementation of multiplierless FFT's in VLSI. The arithmetic scheme is specially tailored for the simple binary coefficients used for these FFT's, which make multiplication trivial. (The class of coefficients dealt with are those that have a maximum of 2 nonzero digits; i.e., sum of 2 integers powers of 2 with each power in the range 0-4.) A single chip processing element for a 4-point DFT (for a radix 4 FFT) with an execution time of 400 ns using a 10 MHz clock has been realized. The chip has an estimated maximum gate count of 11 000 and pin count of 85. It has the capability of achieving a 40 MHz throughput rate for a 1024-point FFT using 20 processing IC's. The use of the 4-point chip to implement higher radix algorithms and various other issues are discussed.

Selective deconvolution: A new approach to extrapolation and spectral analysis of discrete signals

Abstract: This paper describes a new algorithm useful for extrapolation and Fourier analysis of discrete signals that are given by a relative small number of samples. The extrapolation is based on the assumption that the discrete Fourier spectrum shows dominant spectral lines. Involving only FFT, the iterative algorithm is not restricted to one-dimensional signals but can also be applied to higher-dimensional problems. Additional knowledge on the signal like band-limitedness or positivity can easily be taken into account.

Signal enhancement using canonical projection operators

Abstract: A commonly occurring signal processing application is concerned with the task of resurrecting a signal from a noise and distorted measurement of that signal. It is often known that the underlying signal possesses well-defined properties which are obscured through the measurement process. A signal enhancement algorithm is herein developed which slightly modifies the measured signal so that the modified (or enhanced) signal takes on these prescribed properties. As such, the modified signal often provides a more accurate characterization of the underlying signal.

Hidra: A Hierarchical Instrument for Distributed Real-Time Analysis of Biological Signals

Abstract: This work presents a locally distributed common bus multiple-processor system intended to support a hierarchical signal processing scheme for biological signal analysis. Each peripheral unit?the so called preprocessor (PP)?executes real-time signal processsing algorithms over data multiplexed in an input bus. The result of this analysis is transferred to a host computer that integrates the received information from the PP's, saves it in disk when necessary, performs higher level data analysis, and interfaces to the user. The processing of electroencelographic (EEG) data will be used as a case study, due to the multidimensional aspects involved.

Time Domain Signal Processing with the DFT

Abstract: Publisher Summary The discrete Fourier transform (DFT), implemented by one of the computationally efficient fast Fourier transform (FFT) algorithms, has become the core of many digital signal processing systems. These systems can perform general time domain signal processing and classical frequency domain processing. This chapter describes some signal processing applications that use the DFT to perform specific time domain filtering tasks. Two basic filtering tasks can be performed with DFT: (1) convolution or correlation between two arbitrary arrays and (2) narrowband channelization. The DFT gives access to the computational efficiency of the FFT. Some perspectives have evolved that allow classical filtering operations to be implemented by the FFT. The chapter highlights these perspectives. It describes the way in which a judicious choice of window, overlap, block size, and circular indexing, coupled with simple pre- and postprocessing tasks, leads to use of the DFT to perform general time domain processing. It examines the way by which simple pre- and postprocessing tasks significantly enhance the degrees of freedom available to the designer of multichannel processors, the way by which processing parameters are coupled, and the way by which a choice of processing parameters impacts important system considerations such as total computational burden and classical fidelity measures such as channel crosstalk and noise levels.

Evaluation of Image Response Signal Power Resulting from I-Q Channel Imbalance

Abstract: A simple relationship is obtained that gives the ratio of the image to the desired signal in terms of the amplitude and phase imbalance between the I and Q channels in a quadrature transmission and signal reconstruction processor.

A processor for graph search algorithms

Abstract: This report will describe a programmable signal processor with a pipelined arithemetic unit capable of 40 MIPs operation in graph search kernel operations. Thus a fivefold improvement in speech and image processing algorithms can be obtained over conventional architectures The chip was fabricated in a 1.5μm CMOS technology, occupies 43.4mm2and operates at 20MHz.

The Systolic/Cellular System for Signal Processing

Abstract: Va71 0 e,W 06 eo&% /(4#ied these normally unusable times (the clock cycles), data is allowed to flow through cells transparently. A network of East, West, North, and South buses allows data to travel as far as 50 cells away. Many systolic-array architectures only allow direct data transfer between nearest-neighbor processing elements. 1'2 DSP-software development is often a time-consuming and arduous task. Moto-rola's new systolic-array architecture has already reduced this effort. Algorithms are implemented directly in this architecture. Every cell is initialized at least once after each power-up. From that point (power-up) on, the cell performs the same operation every processing cycle. It also gets its input data from the output of an assigned \"neighbor\" cell. This pre-set operation makes it possible to assign the function of each cell directly from a signal-flow diagram. The new systolic-array architecture essentially eliminates sequential software. The software-development tool is written in Pascal for an IBM PC. The basic concept for the development tool is a spread-sheet processor. Algorithms are entered, copied, and replicated just as in any spreadsheet tool. As an added feature, the algorithm can be tested, simulated, and debugged with the same tool. Architecture simulations have reconfirmed that this systolic design performs best on algorithms with strong locality of signal flow.3'4 The date when the architecture will be usable is drawing nearer as logic simulations approach completion.. r e designed the Systolic/Cellu-a controller with a separate program mem-lar System for large classes of ory (see Figure 1). The input data and the *V * linear algebraic and cellular programs for the coprocessor are loaded operations that are used in signal process-from the host into the array memory and ing. It consists of a host and a programma-the program memory, respectively.

Simplifications in multidimensional stability margin computations

Abstract: Previously published algorithms for the computation of multidimensional stability margins of discrete systems require a stability test of these systems before starting the computational algorithm. In this correspondence, it is shown that the multidimensional stability test may be replaced by single-dimensional tests for one kind of stability margin, and can be omitted completely for the second kind of stability margin.

Reconstruction from Fourier transform phase with applications to speech analysis

Abstract: This paper addresses the problem of signal reconstruction from Fourier transform phase. In particular, we examine two aspects of this problem. First, we discuss signal reconstruction from the phase spectrum of the short-time Fourier transform(STFT). Next, we examine the problem of signal recovery from partial phase information. We present the results of our studies on reconstruction from partial phase and discuss the application of these results in speech analysis and coding.

Three element digital control system

Abstract: A universal three-element digital control system is described which forms a proportional signal, an integral signal and a derivative (differential) signal from an error signal and combines such signals to provide a controlling output signal to a device being controlled. The error signal is the difference between the actual signal, representative of the actual condition of the device being controlled, and the setpoint, which is representative of the desired condition. The proportional signal is proportional to the error signal. The integral and differential signals can be approximated by combining the previous error signals with the present error signal. Offset and multiplying elements are provided by which each of the signals can be offset or proportionalized to customize the control system for a particular application.