Showing papers on "Multidimensional signal processing published in 1977"

A unified approach to short-time Fourier analysis and synthesis

Abstract: Two distinct methods for synthesizing a signal from its short-time Fourier transform have previously been proposed. We call these methods the filter-bank summation (FBS) method and the overlap add (OLA) method. Each of these synthesis techniques has unique advantages and disadvantages in various applications due to the way in which the signal is reconstructed. In this paper we unify the ideas behind the two synthesis techniques and discuss the similarities and differences between these methods. In particular, we explicitly show the effects of modifications made to the short-time transform (both fixed and time-varying modifications are considered) on the resulting signal and discuss applications where each of the techniques would be most useful The interesting case of nonlinear modifications (possibly signal dependent) to the short-time Fourier transform is also discussed. Finally it is shown that a formal duality exists between the two synthesis methods based on the properties of the window used for obtaining the short-time Fourier transform.

A new phase unwrapping algorithm

Abstract: A new phase unwrapping algorithm is proposed that combines the information contained in both the phase derivative and the principal value of the phase into an adaptive numerical integration scheme. This new algorithm has proven itself to be very reliable and it can be easily incorporated in standard homomorphic signal processors.

Fundamentals of digital array processing

Abstract: With the advent of high-speed digital electronics, it has become feasible to use digital computers and special purpose digital processors to perform the computational tasks associated with signal reception using an antenna or directional array. The purpose of this paper is mainly tutorial, to describe mathematically and intuitively the fundamental relationships necessary to understand digital array processing. It is hoped that those readers with a background in antenna theory or array processing will see some of the advantages digital processing can offer, while those with a background in digital signal processing recognize the array processing area as a potential application for multi-dimensional signal processing theory.

Ambiguity function display: an improved coherent processor.

Abstract: A coherent optical processor for displaying a signal’s ambiguity function is described. The required time delay is realized by 45° rotations of two identical input transparencies and the Doppler shift by a 1-D Fourier transformation. The entire ambiguity function is displayed in the output (Doppler shift-time delay) plane. Examples of the optically computed ambiguity function for single and double pulse signals are shown to be in excellent agreement with theory. Advantages of this approach over other schemes and possible extension to real time processing are also discussed.

New algorithms for digital convolution

Abstract: It is shown how the Chinese Remainder Theorem (CRT) can be used to convert a one-dimensional cyclic convolution to a multi-dimensional convolution which is cyclic in all dimensions. Then, special algorithms are developed which, compute the relatively short convolutions in each of the dimensions. The original suggestion for this procedure was made in order to extend the lengths of the convolutions which one can compute with number-theoretic transforms. However, it is shown that the method can be more efficient, for some data sequence lengths, than the fast Fourier transform (FFT) algorithm. Some of the short convolutions are computed by methods in an earlier paper by Agarwal and Burrus. Recent work of Winograd, consisting of theorems giving the minimum possible numbers of multiplications and methods for achieving them, are applied to these short convolutions.

Method for performing complex-valued linear operations on complex-valued data using incoherent light.

Abstract: Under normal circumstances, the operations achievable by means of an incoherent optical data processing system are limited to superposition integrals (or, as a special case, convolution integrals) involving real, nonnegative impulse responses and real, nonnegative input data. This restriction arises due to the linearity of such systems in intensity, rather than in complex amplitude. The class of achievable operations can be broadened to include real bipolar spread functions if the results of two nonnegative operations are subtracted, or if a phase switching interferometer is employed. Recently, Lohmann has described a method whereby complex-valued impulse responses can be applied to complex-valued input data, yet the system is still incoherent. We wish to describe here an alternative approach which also allows complex-valued spread functions to be applied to complex-valued input data with an incoherent optical system. The operation to be performed is described mathematically by

Linear space-variant optical processing of 1-D signals.

Abstract: In the past, most optical data processing systems have been restricted to performing linear space-invariant operations. However, a wide class of interesting data processing operations require linear space-variant filtering. Three methods for performing linear space-variant processing of 1-D inputs are described. Experimental results obtained with all three systems are presented, and their relative advantages and disadvantages are discussed.

Space-variant processing of 1-D signals.

Abstract: Two general schemes for 1-D space-variant processing are proposed. The direct output display scheme gives the space-variant system output along a line in the processor’s output plane. The output spectrum display scheme directly computes the space-variant system’s output spectrum. Both of these schemes utilize a 1-D input and a line spread function mask. Example applications and experimental results are also presented.

Integer weighted impulse equivalent coded signal processing apparatus

Abstract: A signal processing apparatus for use in data communications systems where the transmitted signal is subject to the effects of short duration interference, such as impulse noise, or for use in data recording systems where recorded data is subject to the effects of imperfections in the recording media, wherein a coded transformation is performed on an input signal to the apparatus in accordance with a selected time distribution and selected multi-level, integer related weighting functions to produce a coded signal. A decoder can be used to reversibly transform such signal so as to substantially reproduce the input signal in a manner such that the effects of such noise and recording imperfections are minimized.

Hardware realization of digital signal processing elements using the residue number system.

Abstract: In the past, hardware realization of digital signal processing elements have been based upon binary arithmetic concepts. Because of the dependence between digits in binary arithmetic operations, the hardware required to construct arithmetic elements is cumbersome. In the residue number system, arithmetic operations can be performed with complete independence between digits and a corresponding reduction in hardware complexity. In fact, using current technology, arithmetic operations can be carried out using arrays of look-up tables placed in high density ROMs. This paper discusses the application of the residue number system to realizing digital signal processing elements using such arrays and advantages and disadvantages over conventional realizations are discussed. Examples are given of recursive filter and FFT butterfly element realization.

Recursive-like adaptive echo canceller

Abstract: RECURSIVE-LIKE ADAPTIVE ECHO CANCELLER Abstract of the Disclosure The circuit complexity of a closed-loop echo cancellation system for use in a two-way communication circuit is reduced by employing a second adjustable signal processing network of the transversal type positioned in the control loop to emulate the characteristic of a recursive adjustable signal processing network. The two signal processing networks in the control loop are adjusted simultaneously to effect echo cancellation. The second signal processing network compensates for the effect of transmission poles in the echo return path and reduces the duration of the impulse response of the echo return path significantly so that the first signal processing network in the control loop is greatly simplified. A third signal processing network of the recursive type is adjusted in accordance with the internal settings of the second net-work to perform signal processing inverse to that of the second network. The recursive network is utilized to provide a clear signal path through the echo cancellation system which is essentially free of echo.

Acoustic-optic technique for processing many signals simultaneously

Abstract: An acousto-optic apparatus utilizing multiplexing techniques, for obtaininghe correlation of N pairs of signals. First and second sets of signals are combined in a piezoelectric crystal, and each signal in the first set is correlated only with its pair signal in the second set, that is, with the signal in the second set which has the same R.F. frequency. Each signal is a composite signal comprised of an envelope modulating an R.F. signal, and when a laser beam is directed across the interaction area of the crystal and directed onto a square law detector, the correlation of the envelopes of the N pairs of signals is obtained.

Parallel Array Processors for Digital Image Processing

Abstract: A major drawback of digital computer image processing is the large computation time required. On the other hand, its flexibility, programmability and computational accuracy make it desirable to use digital processing. Advances in technology of LSI circuitry have now made it possible to increase strongly the computational power of image processing systems by combining many ‘micro computers’ or processing elements to array processors. We discuss several concepts of connecting such small computers and integrating them into a system, and then concentrate on the ‘PEAC’ structure which was closely investigated at PFH. Its application to various image-processing methods such as point operations, neighbourhood operations, guided boundary detection using prior knowledge, and object reconstruction from projections are discussed. In almost all applications a speed-up ratio of k can be achieved, where k is the number of processing elements.

Optical signal processing apparatus

Abstract: Signal processing apparatus having the capability to perform simultaneous space-time processing of sonar, radar and similar time-varying signals, and to effect the Fourier transform of multiple time-varying signals through electro-optical photoelastic means, photoconductive means, or photoemissive means.

Deconvolution of cyclostationary signals

Abstract: Two algorithms are presented for the deconvolution of a cyclostationary (CS) signal which has been distorted by passage through an unknown linear, time-invariant system. It is necessary to know the statistics of the CS process, but no assumptions about the distorting system are required. Results of the application of the algorithms are presented as well as a discussion of the algorithms' efficiency in the presence of noise.

Acousto-Optic Signal Processors

Abstract: Acousto-optic cells have found a major application in providing compact real-time electrical to optical transducers for optical signal processing systems(1). Such acousto-optic devices with bandwidths up to 1.0 GHz(2) and time bandwidth products exceeding 1000 may be configured with other optical components and devices to perform signal spectrum analysis, correlation, and signal sorting. This paper will present a conceptual overview of the principal acousto-optic techniques available for processing of wideband electronic signals.

A Digital Method of Frequency Multiplication and Its Application to Numeric Spectrum Analysis of Periodic Signals

Abstract: A digital way to produce an integral multiple of the frequency of periodic trigger pulses is described. This procedure is used to generate the sampling pulses for the ADC of a time-series analyzer. The device which implements this method is called sampling frequency generator (SFG). A comparison is made between this digital method and the analog frequency multiplication method by means of a PLL.

A unique hardware and software approach for digital signal processing

Abstract: A novel concept for digital signal processing using universal hardware and flexible software is presented. A universal signal processor (USP) offers multiprocessing facilities with multiple function blocks for data and structured data processing. The basic components such as the CROSSBUS, the input/output processor, the data and structured data processor and the instruction processor are build with standard microprocessor slices. The concept of software is based on the high level language SIPROL (signal processing language) which is derived from PASCAL. The main differences with respect to the manifold problems in digital signal processing are outlined. Examples are presented which illustrate the proposed concept.

Fast Fourier Transform processor using serial processing and decoder arithmetic and control section

Abstract: A signal processor for use in a small, lightweight radar-guided missile to provide a discrete Fast Fourier Transform (FFT) on received radar return signals. The radar return signal are converted into a sequence of binary digits enabling a simple decoder to perform complex addition and subtraction processing, thereby minimizing the space and complexity of the signal processor.

Method and apparatus for obtaining the doppler transform of a signal

Abstract: Method and apparatus for obtaining the doppler transform of a one-dimensional linear signal by re-arranging the signal into a two-dimensional raster form image pattern and then obtaining an optical linear transformation of the two-dimensional image. An optical circuit is provided for carrying out the transformation and is designed to process the signal for a large number of doppler levels in rapid succession without it being necessary to rescan the initial signal each time as in the prior art. Accordingly, a substantial reduction in processing time is achieved. The invention has been developed primarily for use in locating the position of underwater objects through the use of sonar, but has application in a variety of other data processing fields.

One-Dimensional To Two-Dimensional And Two-Dimensional To One-Dimensional Mappings In Optical Signal Processing

Abstract: 1-D to 2-D mappings have been used in optical signal processing to increase the information throughput of optical systems for 1-D signals and to allow shift-variant processing of 1-D signals. We review two examples of such mappings: the spectral analysis of raster recorded signals, and frequency-variant spectral analysis. We then present two new optical signal processing operations where 2-D signals are mapping into 1-D formats for processing: a method for general space-variant processing of 2-D signals, and a novel nonframing video imaging technique.© (1977) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Digital vs. optical techniques in synthetic aperture radar data processing

Abstract: The principal of SAR image-formation is reviewed in preparation for a discussion of both optical and digital processing techniques. The tilted-plane optical-processing approach is presented as being representative of optical techniques. Since the newer digital approaches can take several forms, three classes of digital processors are examined: direct convolution, frequency multiplexing, and frequency analysis of dechirped data. A subjective listing of the relative merits for both processing media is presented. Both are found to be technically viable. The final choice will depend primarily upon the application requirements.

Trade-Offs In Optical Computing

Abstract: The optical analog computer offers the user a very high -speed one -dimensional or two -dimensional system for conducting spectrum analysis, matched filtering, or correlation detection. This type of computer offersa significant advantage in hardware performance (equivalent bits per second per dollar) over the digitalcomputer in certain important signal- processing areas.IntroductionTechnology often places stringent limitations on the approach taken to a particular signal processing task. One usually turns to the digital computer to conduct signal analysis. This technology provides theuser with the capability of performing calculations to essentially any degree of precision with almost in-finite flexibility as to both type and scope of the problem addressed. The user also benefits from ease ofprogramming and from the transferability of software. This is due to the universality of most major program-ming languages and to the general availability of digital computing facilities.In certain special cases, however, the signal processing task makes demands which the digital computer

Optical Signal Processing Applications of the Folded Spectrum

Abstract: The two-dimensional optical Fourier transform of a raster recorded input electrical signal has been shown to result in a "folded spectrum." Selected examples and applications of this optical signal processor in signal demodulation and radar signal processing are discussed.

Optical Processing In Radionuclide Tomographic Image Reconstruction

Abstract: Optical and digital processing of tomographic data is presented and discussed in the context of a Fourier reconstruction algorithm applied to phantom radionuclide sources of nuclear medicine. The point spread function of the reconstruction process is discussed in relation to the angular sampling of frequency space and investigated using coherent optical techniques. Approximations due to gammaray attenuation in the source and the non-stationarity of the point spread function of the detector system are also presented.