A method for filtering a numerical input signal sampled at a sampling frequency in order to obtain a filtered signal, the method being implemented by a system, the system being a communication system, a countermeasure system or a detection system, the system comprising an antenna and a processing chain, the method including:
- receiving an input signal by the antenna,
- converting the input signal into an output signal via the processing chain, the processing chain comprising at least one filter, the at least one filter comprising a transmitter, a first processing channel, a second processing channel and a mixer, wherein the first processing channel comprising a first adder, a second adder, a Fast Fourier Transform (FFT) circuit, an Inverse Fast Fourier Transform (IFFT) circuit, a multiplier, wherein the second processing channel comprising a first adder, a second adder, a FFT circuit, an IFFT circuit, a multiplier, wherein the converting includes:
- transmission, via the transmitter, of the input signal over the first and second processing channels,
- obtaining a first output signal through an implementation of first operations on the first processing channel, the first operations including:
- a first processing of the input signal to obtain a processed signal, via the first adder of the first processing channel,
- applying a discrete Fourier transform to N/2 points on the processed signal, via the FFT circuit of the first processing channel, each point of a spectrum of the processed signal corresponding to even indices of a spectral analysis at N points of the processed signal and being identified in a bijective manner by an index k, k being an even number between 0 and 2*M−1, with M=N/2,
- a second processing of the points of the spectrum of the processed signal in order to obtain first selected points, via the multiplier of the first processing channel,
- an application of an inverse discrete Fourier transform to N/2 points, via the IFFT circuit of the first processing channel, on the first selected points in order to obtain a first signal, and
- a third processing of the first signal in order to obtain the first output signal, via the second adder of the first processing channel, and
- obtaining a second output signal through an implementation of second operations on the second processing channel, the second operations including:
- a first processing of the input signal to obtain a processed signal, via the first adder of the second processing channel, wherein the first processing of the second operations on the second processing channel includes an operation for addition of the input signal shifted by N/2 points and of the input signal shifted by N points,
- applying a discrete Fourier transform to N/2 points on the processed signal, via the FFT circuit of the second processing channel, each point of the spectrum of the processed signal corresponding to odd indices of a spectral analysis at N points of the processed signal and being identified in a bijective manner by an index k, k being an odd number between 0 and 2*M−1,
- a second processing of the points of the spectrum of the processed signal in order to obtain second selected points, via the multiplier of the second processing channel,
- an application of an inverse discrete Fourier transform to N/2 points, via the IFFT circuit of the second processing channel, on the second selected points in order to obtain a second signal, and
- a third processing of the second signal in order to obtain the second output signal, via the second adder of the second processing channel, and
- recombination, via the mixer, of the first output signal and the second output signal, to obtain the filtered signal.