Abstract

This article provides a review and deeper insight on the fundamentals and main design trade-offs of a new method for joint time-frequency analysis of broadband signals, namely, the time-mapped spectrogram (TM-SP). This method involves a temporal periodic sampling of the signal under test (SUT) followed by chromatic dispersion under a Talbot condition. Through this scheme, the time-changing spectrum of the input SUT, namely, its short-time Fourier transform (or SP), is continuously mapped along the time domain, at the sampling rate. The time and frequency resolutions of the resulting SP are respectively dependent on the spectral and temporal width of the sampling pulses, though the latest may be limited by the detection bandwidth. Additionally, the obtained spectrogram is heavily oversampled, ensuring a gap-free spectral analysis, and providing additional opportunities to relax the detection device specifications. A photonic implementation of the concept is discussed, and numerically and experimentally demonstrated, validating our central theoretical findings and predictions. The method enables real-time spectral analysis of GHz-bandwidth arbitrary microwave signals with nanosecond resolutions, fulfilling the performance requirements across many scientific and technology applications.

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