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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TL;DR: In this paper, a general relation between the least mean square (LMS) algorithm and the discrete orthogonal transforms is established, and it is shown that the LMS algorithm could provide a means for the calculation of forward and inverse orthogonality by properly choosing the input vector and adaptation speed.
Abstract: A general relation between the least mean square (LMS) algorithm and the discrete orthogonal transforms is established. Discrete orthogonal transforms, including the discrete Fourier transform (DFT), the discrete Hartley transform (DHT), the discrete cosine transform (DCT), the discrete sine transform (DST), and the Walsh-Hadamard transform (WHT), etc. are extensively used in signal and image processing. It is shown that the LMS algorithm could provide a means for the calculation of forward orthogonal transforms as well as inverse orthogonal transforms by properly choosing the input vector and adaptation speed. >
18 citations
TL;DR: The coding method used for the comparison utilizes a marginal bit-allocation scheme and Lloyd-Max quantizer as discussed by the authors, and the discrete cosine transform outperforms the other three transforms based on the mean-square quantization error.
Abstract: The coding method used for the comparison utilizes a marginal bit-allocation scheme and Lloyd-Max quantizer. Gamma, Laplacian, and Gaussian models are compared for the distribution of the transform coefficients. The discrete cosine transform outperforms the other three transforms based on the mean-square quantization error. >
18 citations
TL;DR: This work is concerned with improving the quality of signal localization for the short-time Fourier transform by properly adjusting the size of its analysis window over time.
Abstract: This work is concerned with improving the quality of signal localization for the short-time Fourier transform by properly adjusting the size of its analysis window over time. The adaptation procedure involves the estimation of an area in the time-frequency plane which is more compact than the support of the fixed-window spectrogram. Then, at each time instant, the optimal window is selected such that the signal energy is maximized within the identified area. The proposed method achieves its objectives, and can compare favorably with alternative time-adaptive spectrograms as well as with advanced quadratic representations.
18 citations
TL;DR: A fast discrete Fourier transform (DFT) computing algorithm used in situations where part of the data is zero and only the first transform elements are to be calculated is proposed.
Abstract: A fast discrete Fourier transform (DFT) computing algorithm used in situations where part of the data is zero and only the first transform elements are to be calculated is proposed. The method is based on the pruning of a split-radix decimation-time (DIT) fast Fourier transform (FFT) diagram. It has the advantage of providing gains as a result of pruning computation and the use of a split radix. >
18 citations
TL;DR: It is shown that the number of data points the arithmetic Fourier transform (AFT) needs for an N-point Fouriertransform is proportional to N/sup 2/.
Abstract: It is shown that the number of data points the arithmetic Fourier transform (AFT) needs for an N-point Fourier transform is proportional to N/sup 2/. Thus, for example, while a standard fast Fourier transform algorithm requires 1024 samples to yield 1024 spectral components, AFT would take more than 300000 samples to do the same job. >
18 citations