This research focus is dedicated to real-time analog signal processing techniques in frequency shift loops. We have in particular shown that a frequency shift loop, in the case where the product shift frequency * travel time of the loop is an integer, generates an output signal which reproduces in time, the spectrum of the input signal ("frequency to time mapping"). This property makes it possible, in a purely analog way, to produce the Fourier transform of time signals, with a frequency resolution of a few tens of kHz. Recall that usual Fourier transform techniques in far-field conditions only allow resolutions higher than GHz. Recently, we have generalized this concept to the fractional Fourier transform in real time. When the product shift frequency * travel time of the loop has a non-integer value - but close to an integer -, the system realizes the fractional Fourier transform of the input signal. This allows in particular the filtering in any arbitrary direction of the time-frequency plane, or the chirp rate measurement of RF signals with linear frequency modulation.

### References:

- C. Schnébelin, and H. Guillet de Chatellus,
*Agile photonic fractional Fourier transformation of optical and RF signals*, Optica 4, 907 (2017).

- H. Guillet de Chatellus, L. Romero Cortés and J. Azaña, Real-time Fourier transformation with kHz resolution, Optics and Photonics News (OPN), Optics in 2016 (2016). .

- H. Guillet de Chatellus, L. Romero Cortés and J. Azaña, Optical real-time Fourier transformation with kHz resolutions, Optica,3, 1 (2016).