Monday, November 28, 2011

Compressive and Noncompressive Power Spectral Density Estimation Software Package and The Continuous-Time Spectrally-Sparse (CTSS) Sampling Toolbox

Michael Lexa, Mike Davies and John Thompson just released two implementations this past week :

Compressive and Noncompressive Power Spectral Density Estimation Software Package

Synopsis
The MATLAB m-files available for download on this page implement the power spectral density (PSD) estimation method proposed in:
M.A. Lexa, M.E. Davies, J.S. Thompson, Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples , 2011, Available on arXiv.
The method estimates the PSD of bandlimited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and applies to spectrally sparse and nonsparse power spectra alike. For sparse density functions, compressed sensing theory is applied and the resulting compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. The estimator does not require signal reconstruction and can be directly obtained from solving either a least squares or a nonnegative least squares problem. The estimates are piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. The estimates are statistically consistent, and the method is widely applicable.
The software allows one to reproduce the three examples given in the paper. Specific details are provided in the README.pdf file included in the download.
Note that the software is meant for researchers who want to quickly understand and experiment with the proposed method. Consequently, the MATLAB scripts have no error handling capabilities and will "break" if incorrect parameters values are entered or if assumptions are violated.

and

The Continuous-Time Spectrally-Sparse (CTSS) Sampling Toolbox

Synopsis
The CTSS Sampling Toolbox is a collection of MATLAB m-files implementing three sub-Nyquist, uniform sampling techniques for acquiring continuous-time spectrally-sparse signals. Two of the techniques, the Random Demodulator (RD) and the Modulated Wideband Converter (MWC), leverage ideas from the theory of compressed sensing. The third, the Multi-coset (MC) Sampler, predates compressed sensing, but shares many commonalities with the MWC.
The RD, the MWC, and the MC Sampler were originally proposed in the following works:

J.A. Tropp, J.N. Laska, M.F. Duarte, J.K. Romberg, and R.G. Baraniuk, Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals, Information Theory, IEEE Transactions on , vol. 56, no. 1, pp. 520-544, Jan 2010.

M. Mishali and Y.C. Eldar, From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals, Selected Topics in Signal Processing, IEEE Journal of, vol. 4, no. 2, pp. 375-391, Apr 2010.

Ping Feng, Universal Minimum-Rate Sampling and Spectrum-Blind Reconstruction for Multiband Signals, Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL U.S.A., 1997.

P. Feng and Y. Bresler, Spectrum-Blind Minimum-Rate Sampling and Reconstruction of Multiband Signals,Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing, vol. 3, pp. 1688-1691, May 1996.

The toolbox is meant for researchers who want to quickly understand, experiment, and compare these sampling systems. Consequently, the MATLAB scripts have minimal error handling capabilities and will "break" if incorrect parameters values are entered or if assumptions are violated.