Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion

A spectrally sparse signal of order $r$ is a mixture of $r$ damped or undamped complex sinusoids. This paper investigates the problem of reconstructing spectrally sparse signals from a random subset of $n$ regular time domain samples, which can be reformulated as a low rank Hankel matrix completion problem. We introduce an iterative hard thresholding (IHT) algorithm and a fast iterative hard thresholding (FIHT) algorithm for efficient reconstruction of spectrally sparse signals via low rank Hankel matrix completion. Theoretical recovery guarantees have been established for FIHT, showing that $O(r^2\log^2(n))$ number of samples are sufficient for exact recovery with high probability. Empirical performance comparisons establish significant computational advantages for IHT and FIHT. In particular, numerical simulations on $3$D arrays demonstrate the capability of FIHT on handling large and high-dimensional real data

High Current Matching over Full-Swing and Low-Glitch Charge Pump Circuit for PLLs

A high current matching over full-swing and low-glitch charge pump (CP) circuit is proposed. The current of the CP is split into two identical branches having one-half the original current. The two branches are connected in source-coupled structure, and a two-stage amplifier is used to regulate the common-source voltage for the minimum current mismatch. The proposed CP is designed in TSMC 0.18µm CMOS technology with a power supply of 1.8 V. SpectreRF based simulation results show the mismatch between the current source and the current sink is less than 0.1% while the current is 40 µA and output swing is 1.32 V ranging from 0.2 V to 1.52 V. Moreover, the transient output current presents nearly no glitches. The simulation results verify the usage of the CP in PLLs with the maximum tuning range from the voltage-controlled oscillator, as well as the low power supply applications

Geometric deformation and redshift structure caused by plane gravitational waves

The curved spacetime induced by gravitational waves can give rise to visual effects such as geometric distortions and redshift structures in the observed image. By establishing a mapping from the object's surface coordinates to the observer's screen coordinates, we study these effects in the context of plane gravitational waves. The simulation reveals that the image of an object doesn't merely seem compressed or stretched, but rather appears twisted and wobbled. Furthermore, the redshift structure on the object's surface appears to rotate as a whole. This outcome offers an intuitive depiction of the lensing effect in plane gravitational wave spacetimes.Comment: 6 pages 2 columns, 3 figure