Device for calculating a discrete fourier transform and its application to pulse compression in a radar system
First Claim
1. A device for calculating a discrete Fourier transform (DFT) on a moving temporal window of a duration T, providing N components (Xm+1) of said DFT using N samples (xm+N) of an input signal from which it is sought to calculate said DFT, wherein N is an integer chosen to be a multiple of four, said device comprising:
- N stages, each supplying one of said components defined by;
##EQU40## where k is an index of the stage, with 0≦
k<
N, and m is an index of said window;
first means for performing a complex rotation required by equation (3), in a pre-rotation operation solely in a first quadrant of a complex plane and a supplementary prerotation corresponding to an integer number of quadrants, said first means including;
N'"'"' complex pre-rotation means with N'"'"'=N/4, each said complex pre-rotation means comprising a first complex rotation operator receiving said samples and performing a rotation in the first quadrant for N'"'"' possible values respectively by the N'"'"' complex rotation operators of said N'"'"' complex pre-rotation means (B),said first means further including second means for selecting one of said N'"'"' values given by the N'"'"' complex pre-rotation means; and
third means for applying a supplementary pre-rotation specific to said stage and output means coupled between outputs of said N'"'"' complex prerotation means and said second means.
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Abstract
A device for calculating a discrete, moving window and non-recurrent Fourier transform, especially applicable to the processing of a pulse compression radar signal. The device includes N stages which, on the basis of samples of the input signal, each give a signal of the form: ##EQU1## where k is the index of the stage (O<k<N), m the index of the window and N the number of samples in the window, N being a multiple of four. The complex rotations of the expressions (1) and (3) are each broken down into a rotation in the first quadrant of the complex plane, a rotation common to N stages and a supplementary rotation specific to each stage, achieved by addition-subtraction.
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Citations
10 Claims
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1. A device for calculating a discrete Fourier transform (DFT) on a moving temporal window of a duration T, providing N components (Xm+1) of said DFT using N samples (xm+N) of an input signal from which it is sought to calculate said DFT, wherein N is an integer chosen to be a multiple of four, said device comprising:
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N stages, each supplying one of said components defined by;
##EQU40## where k is an index of the stage, with 0≦
k<
N, and m is an index of said window;first means for performing a complex rotation required by equation (3), in a pre-rotation operation solely in a first quadrant of a complex plane and a supplementary prerotation corresponding to an integer number of quadrants, said first means including; N'"'"' complex pre-rotation means with N'"'"'=N/4, each said complex pre-rotation means comprising a first complex rotation operator receiving said samples and performing a rotation in the first quadrant for N'"'"' possible values respectively by the N'"'"' complex rotation operators of said N'"'"' complex pre-rotation means (B), said first means further including second means for selecting one of said N'"'"' values given by the N'"'"' complex pre-rotation means; and third means for applying a supplementary pre-rotation specific to said stage and output means coupled between outputs of said N'"'"' complex prerotation means and said second means. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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Specification