Journal ArticleDOI
The nonuniform discrete Fourier transform and its applications in filter design. II. 2-D
Saurabh Bagchi,Sanjit K. Mitra +1 more
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TLDR
In this article, the concept of non-uniform discrete Fourier transform (NDFT) is extended to two dimensions to provide a basic framework for nonuniform sampling of 2-D sequences in the frequency domain.Abstract:
For part I see ibid., vol. 43, no. 6, p. 422-33 (1996). The concept of the nonuniform discrete Fourier transform (NDFT) is extended to two dimensions to provide a basic framework for nonuniform sampling of 2-D sequences in the frequency domain. The 2-D NDFT of a sequence of size N/sub 1//spl times/N/sub 2/ is defined as samples of its 2-D z-transform evaluated at N/sub 1/N/sub 2/ distinct points located in the 4-D (z/sub 1/, z/sub 2/) space. These points are chosen appropriately so that the inverse transform exists. We discuss two special cases in which the choice of the sampling points is constrained so that the 2-D NDFT matrix is guaranteed to be nonsingular, and the number of operations required for computing its inverse is reduced, The 2-D NDFT is applied to nonuniform frequency sampling design of 2-D finite-impulse-response (FIR) filters. Nonseparable filters with good passband shapes and low peak ripples are obtained. This is illustrated by design examples, in which 2-D filters with various shapes are designed and compared with those obtained by other existing methods.read more
Citations
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Journal ArticleDOI
Nonuniform fast Fourier transforms using min-max interpolation
TL;DR: This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm and indicates that the proposed method easily generalizes to multidimensional signals.
Journal ArticleDOI
Efficient dual-tone multifrequency detection using the nonuniform discrete Fourier transform
TL;DR: Using the new algorithm, a single fixed-point DSP can perform ITU-compliant DTMF detection on the 24 telephone channels of a T1 time-division multiple multiplexed telecommunications line.
Journal ArticleDOI
Chaos and NDFT-based spread spectrum concealing of fingerprint-biometric data into audio signals
TL;DR: Experimental and simulation results show that the proposed scheme is robust against common signal processing attacks, secure by secret keys, efficient in performance, and accomplishes perceptual transparency by exploiting the masking effects of human auditory system (HAS).
Journal ArticleDOI
Parabolic Radon transform, sampling and efficiency
TL;DR: In this paper, the authors derived a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general (irregular) sampling for the parabolic Radon transform.
Book ChapterDOI
The Nonuniform Discrete Fourier Transform
Sonali Bagchi,Sanjit K. Mitra +1 more
TL;DR: The Nonuniform Discrete Fourier Transform (NDFT) is provided, which can be used to obtain frequency domain information of a finite-length signal at arbitrarily chosen frequency points and its applications in the design of 1-D and 2-D FIR digital filters are discussed.
References
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Book
Discrete-Time Signal Processing
TL;DR: In this paper, the authors provide a thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete time Fourier analysis.
Book
Two-Dimensional Signal and Image Processing
TL;DR: This text covers the principles and applications of "multidimensional" and "image" digital signal processing and is suitable for Sr/grad level courses in image processing in EE departments.
Journal ArticleDOI
A computer program for designing optimum FIR linear phase digital filters
TL;DR: A general-purpose computer program which is capable of designing a large Class of optimum (in the minimax sense) FIR linear phase digital filters and is shown to be exceedingly efficient.
Journal ArticleDOI
A filter bank for the directional decomposition of images: theory and design
R.H. Bamberger,Mark J. T. Smith +1 more
TL;DR: A directionally oriented 2-D filter bank with the property that the individual channels may be critically sampled without loss of information is introduced and it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed.