Real-time tracking of a waveform frequency content is essential for detection and analysis of fast rare events in communications, radar, radio astronomy, spectroscopy, sensing etc. This requires a method that can provide real-time spectrum analysis (RT-SA) of high-speed waveforms in a continuous and gap-free fashion. Digital signal processing is inefficient to perform RT-SA over instantaneous frequency bandwidths above the sub-GHz range and/or to track spectral changes faster than a few microseconds. Analog dispersion-induced frequency-to-time mapping enables RT-SA of short isolated pulse-like signals but cannot be extended to continuous waveforms. Here, we propose a universal analog processing approach for time-mapping a gap-free spectrogram −the prime method for dynamic frequency analysis− of an incoming arbitrary waveform, based on a simple sampling and dispersive delay scheme. In experiments, the spectrograms of GHz-bandwidth microwave signals are captured at a speed of ~5×109 Fourier transforms per second, allowing to intercept nanosecond-duration frequency transients in real time. This method opens new opportunities for dynamic frequency analysis and processing of high-speed waveforms.

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The ability to detect ultrafast waveforms arising from randomly occurring events is essential to such diverse fields as bioimaging, spectroscopy, radio-astronomy, sensing and telecommunications. However, noise remains a significant challenge to recover the information carried by such waveforms, which are often too weak for detection. The key issue is that most of the undesired noise is contained within the broad frequency band of the ultrafast waveform, such that it cannot be alleviated through conventional methods. In spite of intensive research efforts, no technique can retrieve the complete description of a noise-dominated ultrafast waveform of unknown parameters. Here, we propose a signal denoising concept involving passive enhancement of the coherent content of the signal frequency spectrum, which enables the full recovery of arbitrary ultrafast waveforms buried under noise, in a real-time and single-shot fashion. We experimentally demonstrate the retrieval of picosecond-resolution waveforms that are over an order of magnitude weaker than the in-band noise. By granting access to previously undetectable information, this concept shows promise for advancing various fields dealing with weak or noise-dominated broadband waveforms.

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We report a novel, to the best of our knowledge, all-optical discrete multilevel time-lens (DM-TL) design based on cross-phase modulation (XPM). In this approach, the pump is synthesized such as the quadratic phase modulation is applied to the probe in constant-level time-bins with a maximum phase excursion of 2 π . As a result, a considerable reduction in the required pump power is achieved in comparison to the conventional approach based on a parabolic pump. To illustrate the concept, the proposed DM-TL is here applied to the energy-preserving conversion of a continuous-wave (CW) signal into a train of pulses according to the theory of temporal Talbot array illuminators. We demonstrate CW-to-pulse conversion gains up to 12 at repetition rates exceeding 16 GHz, with a power saving with respect to the conventional parabolic TL that is more significant for increasing conversion gains.