Journal ArticleDOI
The fractional Fourier transform: theory, implementation and error analysis
V. Ashok Narayanan,K.M.M. Prabhu +1 more
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TLDR
It is hoped that this implementation and fixed-point error analysis will lead to a better understanding of the issues involved in finite register length implementation of the discrete fractional Fourier transform and will help the signal processing community make better use of the transform.About:
This article is published in Microprocessors and Microsystems.The article was published on 2003-11-03. It has received 128 citations till now. The article focuses on the topics: Fractional Fourier transform & Non-uniform discrete Fourier transform.read more
Citations
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Proceedings ArticleDOI
Fixed Point error analysis of Radix-4 and Radix-8 FFT algorithms
TL;DR: The analysis of overall quantization loss for the Radix-4 andRadix-8 Fast Fourier Transform (FFT) algorithms is extended to the case where the twiddle factor word length is different from the register word length.
Proceedings ArticleDOI
Chirp FSK based on FRFT for underwater acoustic communication
TL;DR: The paper proposes a novel chirp spread spectrum modulation system based on the explicit relationship between fractional Fourier transform properties of Chirp-FSK signals and their parameters and gives a trade-off between BER and rate of transmission by modulation parameters adjusting.
Proceedings ArticleDOI
Experimental results of long range underwater communication based on chirp-FH signals
TL;DR: A covert underwater acoustic communication method which was robust against channel fading and Doppler shift is proposed and verified through the sea experimental results at range of 60 km.
Proceedings ArticleDOI
Stringed musical instrument recognition using fractional fourier transform and linear discriminant analysis
TL;DR: This paper describes recognition of monophonic isolated sounds of stringed musical instruments using fractional fourier transform based MFCC features and Linear discriminant analysis (LDA) and proposed features based on FRFT and LDA.
Proceedings ArticleDOI
Compressed signal acquisition in wire diagnostic
TL;DR: An alternative ADC based on compressive sensing of the reflected signal in order to overcome the limits of Nyquist and to reduce memory storage is introduced.
References
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Journal ArticleDOI
The fractional Fourier transform and time-frequency representations
TL;DR: The authors briefly introduce the functional Fourier transform and a number of its properties and present some new results: the interpretation as a rotation in the time-frequency plane, and the FRFT's relationships with time- frequencies such as the Wigner distribution, the ambiguity function, the short-time Fouriertransform and the spectrogram.
Book
The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TL;DR: The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.
Journal ArticleDOI
Digital computation of the fractional Fourier transform
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.
Journal ArticleDOI
The discrete fractional Fourier transform
TL;DR: This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions, and is exactly unitary, index additive, and reduces to the D FT for unit order.
Journal ArticleDOI
Effects of finite register length in digital filtering and the fast Fourier transform
Alan V. Oppenheim,C. Weinstein +1 more
TL;DR: The groundwork is set through a discussion of the relationship between the binary representation of numbers and truncation or rounding, and a formulation of a statistical model for arithmetic roundoff, to illustrate techniques of working with particular models.