arXiv subjects

Ray Maleh

Publications and source records attributed to Ray Maleh.

3 recordsLinked to original sources

arXiv2014

Exploiting Spectral Leakage for Spectrogram Frequency Super-resolution

The spectrogram is a classical DSP tool used to view signals in both time and frequency. Unfortunately, the Heisenberg Uncertainty Principal limits our ability to use them for detecting and measuring narrowband signal modulation in wideband environments. On a spectrogram, instantaneous frequency can only be measured to the nearest bin without additional interpolation. This work presents a novel technique for extracting higher accuracy frequency estimates. Whereas most practitioners seek to suppress spectral leakage, we use mismatched windows to exploit such artifacts in order to produce super-resolved spectral displays. We present a derivation of our methodology and exhibit several interesting examples.

cs.IT↗

arXiv2012

RIP Analysis of Modulated Sampling Schemes for Recovering Spectrally Sparse Signals

In this work, we analyze modulated sampling schemes, such as the Nyquist Folding Receiver, which are highly efficient, readily implementable, non-uniform sampling schemes that allows for the blind estimation of a narrow-band signal's spectral content and location in a wide-band environment. This non-uniform sampling, achieved by narrow-band modulation of the RF instantaneous sample rate, results in a frequency domain point spread function that is between the extremes obtained by uniform sampling and totally random sampling. As a result, while still preserving structured aliasing, the modulated sampling scheme is also useful in a compressive sensing (CS) setting. We estimate restricted isometry property (RIP) constants for CS matrices induced by such modulated sampling schemes and use those estimates to determine the amount of sparsity needed for signal recovery. This is followed by a demonstration and analysis of Orthogonal Matching Pursuit's ability to reconstruct signals from noisy non-uniform samples.

cs.IT↗

arXiv2011

Improved RIP Analysis of Orthogonal Matching Pursuit

Orthogonal Matching Pursuit (OMP) has long been considered a powerful heuristic for attacking compressive sensing problems; however, its theoretical development is, unfortunately, somewhat lacking. This paper presents an improved Restricted Isometry Property (RIP) based performance guarantee for T-sparse signal reconstruction that asymptotically approaches the conjectured lower bound given in Davenport et al. We also further extend the state-of-the-art by deriving reconstruction error bounds for the case of general non-sparse signals subjected to measurement noise. We then generalize our results to the case of K-fold Orthogonal Matching Pursuit (KOMP). We finish by presenting an empirical analysis suggesting that OMP and KOMP outperform other compressive sensing algorithms in average case scenarios. This turns out to be quite surprising since RIP analysis (i.e. worst case scenario) suggests that these matching pursuits should perform roughly T^0.5 times worse than convex optimization, CoSAMP, and Iterative Thresholding.

cs.DS↗