INTRODUCTION

The Hilbert transform is a fundamental signal processing function with wide range of applications in radar systems, signal sideband modulators, measurement systems, signal sampling, and many others [1-8]. Fractional Hilbert transforms provide an additional degree of freedom in terms of a variable phase shift, which can meet the special requirements of unilateral communication [2] and confidentiality of hardware keys [3]. In practical applications such as multiplexing and demultiplexing signals, analyzing individual sub-channel spectral components, etc., Hilbert transformers are typically realized as a truncated or windowed version of the ideal Hilbert transform impulse response [5-7]. Therefore, Hilbert transformers covering a wide range of different band pass regions are highly desirable.
Compared to electrical Hilbert transformers that suffer from intrinsic bandwidth bottlenecks, photonic integrated devices have shown advantages in high-speed signal processing. RF photonic Hilbert transformers have been proposed based on fiber Bragg gratings [9-15], micro-ring / micro-disk resonators [16, 17], and integrated reconfigurable microwave processors [18]. However, most of these schemes focus on generating the Hilbert transform of the complex optical fields rather than the actual RF signal. In order to realize highly reconfigurable RF photonic Hilbert transformers, transversal schemes with a high reconfigurability have been investigated [19, 20]. However, the use of multiple discrete laser sources presents limitations in the overall system footprint, processing performance, and the potential for full monolithic integration.
Recently, micro-combs that offer a large number of coherent wavelengths from one compact device have attracted significant interest as a fundamentally powerful tool for microwave processing [8, 21-40] . They have been used for various advanced signal processing [8, 41-64] and neural networks [65-67]. In Ref. [1], we reported a fractional Hilbert transformer with a RF bandwidth ranging from 5 to 9 octaves depending on the fractional order. It was based on a soliton crystal micro-comb with FSR = 48.9 GHz, and 17 taps were selected from the 75 wavelengths generated in the C band as discrete taps.
In this paper, we further demonstrate a photonic Hilbert transformer with variable bandwidth and RF center frequency [1]. It is based on a transversal filter system with a soliton crystal Kerr micro-comb source. In the experimental demonstration, we used 40 comb lines in the C-band [1]. By programming and shaping the comb lines according to calculated tap weights, the center frequency of Hilbert transform was tuned from baseband to 9.5 GHz, and the bandwidth of RF amplitude and phase responses was tuned from 1.2 to 15.3 GHz, confirming the high reconfigurability of our system. The experimental results show good agreement with the theory, confirming the feasibility of our approach towards the realization of high-speed reconfigurable Hilbert transformers with reduced footprint, lower complexity, and potentially reduced cost.