A Constrained Random Demodulator for Sub-Nyquist Sampling
A Constrained Random Demodulator for Sub-Nyquist Sampling
By Andrew Harms, Waheed U. Bajwa, and Robert Calderbank
IEEE Transactions on Signal Processing (2013)
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Andrew  Harms

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The code can be used to reproduce the simulations presented in the associated paper or to run similar simulations. The code uses SpaRSA to calculate the Lasso solution and YALL1 to calculate the basis pursuit solution to finding spectral coefficients.
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Abstract
This paper presents a significant modification to the Random Demodulator (RD) of Tropp et al. for sub-Nyquist sampling of frequency-sparse signals. The modification, termed constrained random demodulator, involves replacing the random waveform, essential to the operation of the RD, with a constrained random waveform that has limits on its switching rate because fast switching waveforms may be hard to generate cleanly. The result is a relaxation on the hardware requirements with a slight, but manageable, decrease in the recovery guarantees. The paper also establishes the importance of properly choosing the statistics of the constrained random waveform. If the power spectrum of the random waveform matches the distribution on the tones of the input signal (i.e., the distribution is proportional to the power spectrum), then recovery of the input signal tones is improved. The theoretical guarantees provided in the paper are validated through extensive numerical simulations and phase transition plots.
Harms, A., W. U. Bajwa, and R. Calderbank, "A Constrained Random Demodulator for Sub-Nyquist Sampling", IEEE Transactions on Signal Processing , 61, 707-723.
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07/22/2014
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