FRFT時(shí)頻變換代碼(參考算法:H.M. Ozaktas, M.A. Kutay, and G. Bozdagi.Digital computation of the fractional Fourier transform.IEEE Trans. Sig. Proc., 44:2141--2150, 1996.)
The frequency domain plays an important role in image
processing to smooth, enhance, and detect edges of images. Although
image data typically does not include imaginary values, the fast Fourier
transform (FFT) has been used for obtaining spectra. In this paper,
the fast Hartley transform (FHT) is used to transform two-dimensional
image data. Because the Hartley transform is real valued, it does
not require complex operations. Both spectra and autocorrelations of
two-dimensional ultrasound images of normal and abnormal livers were
computed.
An important book that cover wavelet domain. It help a lot in understanding wavelets and their applications.
Beside explanations of the transform and application of this, there are also presents the reasons why wavelets are better than Fourier transform.
David Vernon is the Coordinator of the European Network for the Advancement of Artificial Cognitive Systems and he is a Visiting Professor of Cognitive Systems at the University of Genoa. He is also a member of the management team of the RobotCub integrated working on the development of open-source cognitive humanoid robot.
Over the past 27 years, he has held positions at Westinghouse Electric, Trinity College Dublin, the European Commission, the National University of Ireland Maynooth, Science Foundation Ireland, and Etisalat University College.
He has authored two and edited three books on computer vision and has published over eighty papers in the fields of Computer Vision, Robotics, and Cognitive Systems. His research interests include Fourier-based computer vision and enactive approaches to cognition.
He is currently a Professor at Etisalat University College in Sharjah-United Arab Emirates, focusing on Masters programs by research in Computing fields.".[1]
Use
the fast Fourier transform function fft to analyse following signal. Plot the original signal, and the magnitude of its
spectrum linearly and logarithmically. Apply Hamming window to reduce the
leakage.
.
The hamming window can be coded in Matlab as
for n=1:N
hamming(n)=0.54+0.46*cos((2*n-N+1)*pi/N);
end;
where
N is the data length in the FFT.
In this paper we revisit hybrid analog-digital precoding systems with emphasis on their modelling
and radio-frequency (RF) losses, to realistically evaluate their benefits in 5G system implementations.
For this, we decompose the analog beamforming networks (ABFN) as a bank of commonly used RF
components and formulate realistic model constraints based on their S-parameters. Specifically, we
concentrate on fully-connected ABFN (FC-ABFN) and Butler networks for implementing the discrete
Fourier transform (DFT) in the RF domain. The results presented in this paper reveal that the performance
and energy efficiency of hybrid precoding systems are severely affected, once practical factors are
considered in the overall design. In this context, we also show that Butler RF networks are capable of
providing better performances than FC-ABFN for systems with a large number of RF chains.