Real-time Fourier Transformation Based On Bandwidth Magnification

Spectrum analysis is a fundamental tool in many areas today,including wireless communications,radar,electronic countermeasures,etc.For example,in the field of wireless communications,with the continuous development of communication systems,the spectrum existed in the space is becoming more and more dense,and the rational use of resources will become more and more urgent.Therefore,broadband and real-time spectrum analysis are important prerequisites for the rational application of wireless resources.Microwave-photonics is a research field that has been carried out at home and abroad in recent decades.By using high-bandwidth and low-loss photonic devices,it is expected to carry radio frequency signals(RF)onto optical signals to realize RF signal processing.Real-time Fourier Transform(RTFT),also known as Frequency-Time Mapping(FTM),is a very effective method for obtaining broadband RF spectrum.It successfully solved the limitation of common digital devices.The disadvantage of this scheme is that the required dispersion is too large to to achieve sufficient spectral resolution.The main research content of this paper is to improve real-time Fourier transform system.The main work is as follows:First,the basic principle of real-time Fourier transform is introduced.Based on the space-time correspondence principle,through a quadratic phase modulation,the spectrum of input RF signal can be obtained at the output.Then,two real-time Fourier transform schemes are introduced:the dispersion-based real-time Fourier transform scheme and the time-lens based real-time Fourier transform scheme.Through detailed mathematical derivation,we obtained the specific expression of the output signal and the conditions that the relevant parameters in the system need to meet.Second,improvements based on traditional technology proposed by domestic and foreign scholars are researched.Using time-lens technology to stretch the time domain signal,the RF spectrum analyzer based on time domain amplification technology successfully achieved a frequency resolution of several hundred MHz.Researchers demonstrated a novel solution for kilohertz FTM resolution based on an active fiber cavity with frequency shifted feedback(FSF)to achieve equivalent large dispersion.In addition,researchers realized a frequency resolution of 25 MHz through a passive fiber optical ring.However,those schemes usually suffer from the restrictions of limited observation bandwidth.When the observation bandwidth increases,the observation time window is decreased due to the inherent periodic output,which might cut back the distinguishable frequency points.Therefore,for the broadband RF signal,large-bandwidth oscilloscope is required to realize large instantaneous bandwidth.Third,in order to improve the frequency resolution under the limitation of dispersion,this paper proposed a novel real-time Fourier transform system based on the bandwidth magnification of RF signals.Different from the traditional electro-optical modulation,this scheme introduced a new bandwidth-amplified up-conversion before frequency-time domain mapping.The input RF tones are firstly modulated on an optical frequency comb(OFC)to acquire large numbers of copies of the input spectrum.Then,through a Vernier comb filter(VCF)where its free spectral range(FSR)is slightly different from the frequency comb’s FSR,an optically-carried RF signal is obtained with greatly magnified bandwidth which can be analogous to the model of Vernier caliper.As a result,two RF components with an interval of tens of MHz can be separated by tens of GHz in optical spectrum.Thus,even with conventional dispersion provided by optical fibers,frequency components can be significantly separated and observed in time domain.Fourth,this paper designed a specific experimental system to verify the feasibility of real-time Fourier transform based on the bandwidth magnification of RF signals.From the experimental results,based on the ordinary dispersion of 1500ps/nm provided by DCF,we successfully realized the high linear time-frequency mapping of 60MHz resolution,and the dispersion is equivalently amplified to 1975.5ps/GHz(2.47 x 105 ps/nm),equivalent to 1.45 × 104-km single mode fiber.Moreover,by adjusting the FSR of the OFC,we can reconstruct the frequency resolution.In addition,we can change the sign of the equivalent dispersion by adjusting the position of the line.Compared to the conventional RTFT system based on the same dispersion,the dispersion is equivalently amplified by 165 times by the bandwidth magnification of RF signals.