Analog to information conversion for sparse signals band-limited in
 fractional Fourier transform domain

In today's highly developed information technology era, digital information is ubiquitous, the convenience and intelligence of digital technology have penetrated into many aspects including energy, education, medical care, community and other social fields. It’s building a new digital life for people, and the digital economy has gradually become a new engine of economic growth in China. However, analog is a fundamental property of the nature, most signals occurred in nature are in the form of analog, and the sampling is an inevitable step from analog physical world to digital information world. Nowadays, the sampling plays a crucial role in signal processing and communi-cations. It answered how to convert an analog signal into a sequence of numbers and how to reconstruct the signal by discrete sampled values. When it comes to the sampling theory, it can be traced back to the Cauchy era. Until now, the research on sampling far from the end.
    The traditional Shannon sampling theory aims at the band limited signal, on the basis that the sampling interval can not lead to the spectrum aliasing, the sampling rate is limited by a bottleneck of twice the signal bandwidth. In recent years, there is a kind of effective method can solve this bottleneck, which is inspired by the compressed sensing theory. It makes full consideration and use of the characteristics of analog signal during designing the sampling and reconstruction system. In view of this, based on compressed sensing theory, a new underdetermined sampling framework called analog-to-information conversion (AIC) was proposed.
    The research team led by Associate Professor Shi Jun in Communication Research Center, Harbin Institute of Technology, is working on Analog to information conversion based on fractional Fourier transform (FRFT). The FRFT can show a series of characteristics of signal between time domain and frequency domain. Using this feature, they proposed the signal sparse representation based on the FRFT. For some signals whose frequency are continuous, it may be sparse in fractional Fourier domain under certain angle, such as the Chirp signal which is widely used in radar and communication. Based on the compressed sensing theory, a sub-Nyquist sampling system based on fractional Fourier transform domain was constructed. As shown in the Fig1, a more generalized AIC for band-limited sparse signal in FRFT domain was proposed, the traditional AIC scheme in Fourier domain is its special form. The extension of the traditional AIC to the generalized AIC scheme is not an end, the most important thing is that it can overcome the limitation of signal model in the traditional AIC, in which the signal must be sparse band-limited in Fourier domain. At the same time, it has important theoretical significance and engineering application value.

The diagram of AIC in fractional Fourier domain

About Team
The research team of Associate Professor Shi Jun in Communication Research Center, Harbin Institute of Technology in China, mainly focus on Fractional-order signal processing theory and methods, sampling and reconstruction theory, communication system in transform domain, etc. The research members are Liu Xiaoping, Fang Xiaojie, Song Weibin, Deng Yiqiu, Sun Nan, Zhang Shengru, Sha Xuejun and Zhang Qinyu. In recent years, two monographs on fractional signal processing have been published. More than 40 academic papers have been published in IEEE Transactions on Signal Processing, IEEE Signal Processing Letters, Signal Processing Letters and other international academic conferences in the field of Signal Processing. Among them, more than 20 papers were retrieved by SCI and EI, and more than 20 papers were retrieved by EI. Applied for 10 national invention patents, 4 items have been authorized. In addition, 2 National 973 Projects, 2 National Natural Science Foundation Projects, 1 National Major Science and Technology Project, 1 MIIT National Defense Foundation Pre-Research Project, and 1 CASC Joint Innovation Project have been completed. At present, 1 National Natural Science Foundation Project, 1 National Defense Science and Technology Project Fund, and 1 Provincial Natural Science Fund are under research. Won the second prize in the provincial natural sciences.

Song W B, Zhang S R, Deng Y Q, et al. Analog to information conversion for sparse signals band-limited in fractional Fourier transform domain[J]. Opto-Electronic Engineering, 2018, 45(6): 170740.