Double odd discrete fourier transformer
AssigneeTelecommunications Radioelectriques et Telephoniques T.R.T.
InventorGeorges Bonnerot
Life of this patent
Estimating the term…
Abstract
An arrangement for computing the discrete Fourier transform intended for converting N samples of a real signal in the time domain to N real Fourier coefficients. This device is implemented with a conventional Fourier transformer of the order N/4, to which an input computer unit and an output computer unit are connected in which a small number of multiplications of complex numbers is performed.
Claims6
An arrangement for computing Fourier coefficients C.sub.n of a real input signal corresponding to a time sequence of N time-and amplitude discrete samples X.sub.k, comprising
- an input for supplying N discrete samples X.sub.k ;
- a preprocessing device connected to said input, and comprising a storage device having two outputs for producing N/4 signal samples X.sub.i, and N/4 signal samples X.sub.(N/2) + i, respectively, said signal samples X.sub.i and X.sub.(N/2) + i being shifted in relation to one another by N/2 samples;
- a first multiplying device connected to said outputs of said storage device and comprising a complex number generator for multiplying signals from said preprocessing device by predetermined complex numbers, and producing an output signal N/4 complex samples Z.sub.i in response to the pairs of output samples X.sub.i, X.sub.(N/2) + i of the storage device and the complex numbers generated by the complex number generator;
- a DFT computer having an input connected to said output of said multiplying device and having an output for producing N/4 complex signals .sigma..sub.q in response to the N/4 complex samples Z.sub.i on said input;
- and
- a second multiplying device and associated second complex number generator means connected to said output of said DFT computer for producing the real Fourier coefficients C.sub.q and the real Fourier coefficients C.sub.(N/2) + q as real and imaginary part respectively of a complex number C.sub.q + jC.sub.(N/2) + q, in response to said signals .sigma..sub.q and the complex numbers generated by said second complex numbers generating means.
An arrangement for computing real signal samples X.sub.k of a real signal from the real Fourier coefficients C.sub.n of the signal comprising
- an input for supplying N Fourier coefficients;
- a preprocessing device connected to said input for processing said N Fourier coefficients, comprising a storage device having two outputs for producing N/4 coefficients C.sub.i and N/4 coefficients C.sub.(N/2) + i respectively, said coefficients C.sub.i and C.sub.(N/2) + i being shifted in relation to one another by N/2 coefficients;
- a first multiplying device connected to said outputs of said storage device, and comprising a complex number generator for multiplying signals from said preprocessing device by predetermined complex numbers, and producing an output signal N/4 complex samples .sigma..sub.i in response to the pairs of output samples C.sub.i, C.sub.(N/2) + i of the storage device and the complex numbers generated by the complex number generator;
- a DFT computer having an input connected to said output of said multiplying device and having an output for producing N/4 complex signals Z.sub.i in response to the N/4 complex samples .sigma..sub.i on said input;
- and
- a second multiplying device and associated second complex number generator means connected to said output of said DFT computer for producing the real Fourier coefficients X.sub.i and the real Fourier coefficients X.sub.(N/2) + i as real and imaginary part respectively of a complex number X.sub.i + jX.sub.(N/2) + i, in response to said signals Z.sub.i and the complex numbers generated by said second complex number generating means.
Dependencies are inferred from the claim text.