Interpolation aims to retrieve missing values. Resulting from the inaccuracy of sensors, channel distortion, and a variety of measurement errors, signals are contaminated with noise. To well interpolate these noisy signals, an adaptive interpolation algorithm is proposed in this work. First, a novel atom selection mechanism, which incorporates the ridge regression problem and the iterative hard-thresholding algorithm, is applied to identify dominant frequencies. The essential time-frequency information is thus precisely extracted. Prolate spheroidal wave functions, which are highly concentrated in the time-frequency plane, are then appropriately modulated. Finally, atoms are refined to form a proper basis dictionary for signal expansion and interpolation. Comprehensive experiments are conducted to validate that the proposed RidIHT algorithm has outstanding performance in interpolating from noisy samples.

This paper presents new theoretical and application aspects on inferring the parameters in integral transforms. An integral transform, e.g., the linear canonical transform (LCT), usually has many parameters. It is a difficult issue to find the optimal parameters of the integer transform. In this work, we propose a generalized inference method to determine the optimal parameters of the LCT and the fractional Fourier transform (FrFT). With proper design of object functions, optimal parameter estimation can be performed effectively and automatically. The LCT with the optimal parameter set can well represent a complex signal and minimize the energy outside of the low-frequency band in terms of the ℒ1or the ℒ2norm. It is applicable in signal processing, filter design, system modeling, and machine learning.

Interpolation and extrapolation are to fill and predict missing values. To perform these works well, the bases that are highly concentrated in the time-frequency plane and match the characteristics of signals should be adopted. In this work, we propose several algorithms to deal with these tasks. Their concepts are based on generalized chirp-modulated and time-frequency division forms of prolate spheroidal wave functions, boasting attracting mathematical properties. Time-frequency divided prolate spheroidal wave functions can well approximate a signal whose energy distributes sparsely in the time-frequency plane. Moreover, generalized chirp modulation can well model a signal whose instantaneous frequency varies with time. Several experiments are conducted and the effectiveness of our proposed algorithms is manifested by the experimental results and quantitative evaluation.

A single controller current balance (SCCB) technique is proposed to achieve the time-multiplexing current balance in voltage-mode multi-phase DC-DC buck converter with only one modulation controller. Thus, the N-I controllers can be removed when the SCCB technique is implemented in the monolithic N- phase DC-DC buck converters for largely decreasing the silicon area and power consumption. In addition, the time-multiplexing current balance scheme can further enhance the current sharing accuracy since the mismatches between different controllers does not exist. Simulated results show that the current difference between each phase can be decreased by over 80 % at both heavy load and light load conditions.