McClellan transformations for two-dimensional digital filtering-Part I: Design
TL;DR: In this article, the design of two-dimensional linear-phase FIR digital filters by transformations of one-dimensional (l-D) filters was discussed, using a technique first presented by McClellan.
Abstract: This paper discusses the design of two-dimensional (2-D) linear-phase FIR digital filters by transformations of one-demensional (l-D) filters, using a technique first presented by McClellan. His original transformations are generalized and several algorithms are presented for the design of the generalized transformations. Examples are included to demonstrate, the versatility of the design method.
Citations
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01 Jun 1979
TL;DR: Methods for the processing of two- dimensional signals which have been sampled as two-dimensional hexagonal arrays are presented and some comparisons between the two methods for representing planar data will also be presented.
Abstract: Two-dimensional signals are normally processed as rectangularly sampled arrays; i.e., they are periodically sampled in each of two orthogonal independent variables. Another form of periodic sampling, hexagonal sampling, offers substantial savings in machine storage and arithmetic computations for many signal processing operations. In this paper, methods for the processing of two-dimensional signals which have been sampled as two-dimensional hexagonal arrays are presented. Included are methods for signal representation, linear system implementation, frequency response calculation, DFT calculation, filter design, and filter implementation. These algorithms bear strong resemblances to the corresponding results for rectangular arrays; however, there are also many important differences. Some comparisons between the two methods for representing planar data will also be presented.
393 citations
TL;DR: An approach to designing multidimensional linear-phase FIR diamond subband filters having the perfect reconstruction property is presented, based on a transformation of variables technique and is equivalent to the generalized McClellan transformation.
Abstract: An approach to designing multidimensional linear-phase FIR diamond subband filters having the perfect reconstruction property is presented. It is based on a transformation of variables technique and is equivalent to the generalized McClellan transformation. Methods for designing a whole class of transformation are given. The approach consists of two parts; design of the transformation and design of the 1-D filters. The use of Lagrange halfband filters to design the 1-D filters is discussed. The modification of a particular Lagrange halfband filter which gives a pair of simple 1-D filters that are almost similar to each other in their frequency characteristics but still form a perfect reconstruction pair is presented. The design technique is extended to other types of two-channel sampling lattice and subband shapes, in particular, the parallelogram and the diagonally quadrant subband cases. Several numerical design examples are presented to illustrate the flexibility of the design method. >
177 citations
Cites methods from "McClellan transformations for two-d..."
...A technique that uses a particular type of McClellan transformation [ 15 ], [12]...
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01 Jun 1977
TL;DR: The purpose of this paper is mainly tutorial, to describe mathematically and intuitively the fundamental relationships necessary to understand 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.
157 citations
TL;DR: In this paper, a variable-weight fusion rule based on the nonsubsampled contourlet transform (NSCT) was proposed to fuse the intensity components of original images in the multiscaled space and obtained in the generalized intensity-hue-saturation (GIHS) frame.
133 citations
Cites methods from "McClellan transformations for two-d..."
...The mapping approach [23,24] first proposed by McClellan effectively controls both the magnitude and phase responses of 2D filters....
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Book•
08 Jan 2009
TL;DR: In this article, Fourier Transforms in Probability, Random Variables and Stochastic Processes are used for time-frequency representation of signal and image synthesis in the context of Fourier analysis.
Abstract: 1. Introduction 2. Fundamentals of Fourier Analysis 3. Fourier Analysis in Systems Theory 4. Fourier Transforms in Probability, Random Variables and Stochastic Processes 5. The Sampling Theory 6. Generalizations of the Sampling Theorem 7. Noise and Error Effects 8. Multidimensional Signal Analysis 9. Time-Frequency Representations 10. Signal Recovery 11. Signal and Image Synthesis: Alternating Projections Onto Convex Sets 12. Mathematical Morphology and Fourier Analysis on Time Sales 13. Applications 14. Appendices 15. Reference
111 citations
References
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01 Oct 1974
TL;DR: A tutorial review of the reconstruction problem and some of the algorithms which have been proposed for its solution, and a number of new algorithms that appear to have some advantages over previous algorithms are presented.
Abstract: In a wide variety of applications it is necessary to infer the structure of a multidimensional object from a set of its projections. There has been a long-standing interest in this problem and a number of different techniques have been proposed. In this paper, we present a tutorial review of the reconstruction problem and some of the algorithms which have been proposed for its solution. In addition, we present a number of new algorithms that appear to have some advantages over previous algorithms. Some comparisons of these algorithms applied to reconstructions of two-dimensional pictures are given. Furthermore, a number of new theoretical results are presented relating to the minimum number of projections necessary for exact reconstruction.
462 citations
TL;DR: It is demonstrated that phase accuracy is extremely important in image processing filters and the hope is that more work will be done on the development of filter design techniques which use phase as well as magnitude specifications.
Abstract: We demonstrate that phase accuracy is extremely important in image processing filters and express the hope that more work will be done on the development of filter design techniques which use phase as well as magnitude specifications.
174 citations
01 Apr 1975
TL;DR: The problems of designing and implementing LSI systems for the processing of 2-D digital data, such as images or geophone arrays, are reviewed and discussed.
Abstract: The problems of designing and implementing LSI systems for the processing of 2-D digital data, such as images or geophone arrays, are reviewed and discussed. This discussion encompasses both FIR and IIR digital filters and with respect to the latter, the issues of stability testing and filter stabilization are also considered. Techniques are also presented whereby such filtering can be accomplished using either 1 or 2-D LSI systems.
135 citations
TL;DR: It is shown that good two-dimensional windows can be obtained by rotating good one- dimensional windows, that is, if w(x) is a good symmetrical one-dimensional window, then w sub 2(x,y) = w(square root of (x squared + y squared)) is aGood circularly symmetrical two- dimensional window.
Abstract: : Two-dimensional windows find applications in many diverse fields, such as the spectral estimation of random fields, the design of two-dimensional digital filters, optical apodization, and antenna array design. Many good one- dimensional windows have been devised, but relatively few two-dimensional windows have been investigated. In this paper we show that good two-dimensional windows can be obtained by rotating good one-dimensional windows. That is, if w(x) is a good symmetrical one-dimensional window, then w sub 2(x,y) = w(square root of (x squared + y squared)) is a good circularly symmetrical two- dimensional window.
118 citations
TL;DR: The theory for designing finite-duration impulse response (FIR) digital filters can readily be extended to two or more dimensions using linear programming techniques, and several of the issues involved in designing two-dimensional digital filters are discussed in this article.
Abstract: The theory for designing finite-duration impulse response (FIR) digital filters can readily be extended to two or more dimensions. Using linear programming techniques, both frequency sampling and optimal (in the sense of Chebyshev approximation over closed compact sets) two-dimensional filters have been successfully designed. Computational considerations have limited the filter impulse response durations (in samples) to 25 by 25 in the frequency sampling case, and to 9 by 9 in the optimal design case. However, within these restrictions, a large number of filters have been investigated. Several of the issues involved in designing two-dimensional digital filters are discussed.
116 citations