Topic
Non-uniform discrete Fourier transform
About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.
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01 May 1982
TL;DR: This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude, for applications such as speech processing.
Abstract: This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude. For applications such as speech processing, these conditions place very mild restrictions on the signal as well as the analysis window of the transform. Examples of such reconstruction for speech signals are included in the paper.
79 citations
01 Dec 1990
TL;DR: By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao.
Abstract: According to Wang, there are four different types of DCT (discrete cosine transform) and DST (discrete sine transform) and the computation of these sinusoidal transforms can be reduced to the computation of the type-IV DCT. As the algorithms involve different sizes of transforms at different stages they are not so regular in structure. Lee has developed a fast cosine transform (FCT) algorithm for DCT-III similar to the decimation-in-time (DIT) Cooley–Tukey fast Fourier transform (FFT) with a regular structure. A disadvantage of this algorithm is that it involves the division of the trigonometric coefficients and may be numerically unstable. Recently, Hou has developed an algorithm for DCT-II which is similar to a decimation-in-frequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phase-modulated discrete Fourier transform (DFT), which may not be performed in-place. In the paper, a variant of Hou's algorithm is presented which is both in-place and numerically stable. The method is then generalised to compute the entire class of discrete sinusoidal transforms. By making use of the DIT and DIF concepts and the orthogonal properties of the DCTs, it is shown that simple algebraic formulations of these algorithms can readily be obtained. The resulting algorithms are regular in structure and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao. By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vector-radix generalisation of the present algorithms, share the in-place and regular structure of their 1-D counterparts.
79 citations
TL;DR: The theoretical basis of the selective Fourier transform technique is developed and experimental results are presented, including comparisons of spectral localization using either the selective fourier transform method or conventional multidimensional Fouriertransform chemical‐shift imaging.
Abstract: We have introduced the selective Fourier transform technique for spectral localization. This technique allows the acquisition of a high-resolution spectrum from a selectable location with control over the shape and size of the spatial response function. The shape and size of the spatial response are defined during data acquisition and the location is selectable through processing after the data acquisition is complete. The technique uses pulsed-field-gradient phase encoding to define the spatial coordinates. In this paper the theoretical basis of the selective Fourier transform technique is developed and experimental results are presented, including comparisons of spectral localization using either the selective Fourier transform method or conventional multidimensional Fourier transform chemical-shift imaging. © Academic Press, Inc.
79 citations
Book•
30 Nov 1998TL;DR: In this article, the NDFT was used to construct a 1-D and 2-D antenna pattern synthesis with Prescribed Nulls, and the Dual-Tone Multi-Frequency Signal Decoding (DTMSD) was proposed.
Abstract: 1. Introduction. 2. The Nonuniform Discrete Fourier Transform. 3. 1-D Fir Filter Design Using the NDFT. 4. 2-D Fir Filter Design Using the NDFT. 5. Antenna Pattern Synthesis with Prescribed Nulls. 6. Dual-Tone Multi-Frequency Signal Decoding. 7. Conclusions. References. Index.
79 citations
TL;DR: A fast and efficient algorithm based on the alternating split Bregman technique is proposed to carry out the optimization with computational complexity of time-frequency (TF) decomposition in the framework of sparse regularization theory.
Abstract: In this paper, time-frequency (TF) decomposition (TFD) is studied in the framework of sparse regularization theory. The short-time Fourier transform is first formulated as a convex constrained optimization where a mixed l1-l2 norm of the coefficients is minimized subject to a data fidelity constraint. Such formulation leads to a novel invertible decomposition with adjustable TF resolution. Then, a fast and efficient algorithm based on the alternating split Bregman technique is proposed to carry out the optimization with computational complexity [N2 log(N)]. Window length is a key parameter in windowed Fourier transform which affects the TF resolution; a novel method is also presented to determine the optimum window length for a given signal resulting to maximum compactness of energy in the TF domain. Numerical experiments show that the proposed sparsity-based TFD generates high-resolution TF maps for a wide range of signals having simple to complicated patterns in the TF domain. The performance of the proposed algorithm is also shown on real oil industry examples, such as ground roll noise attenuation and direct hydrocarbon detection from seismic data.
78 citations