Sensitivity of the random demodulation framework to filter tolerances

The aim of the present paper is to demonstrate the impact of low-pass filter non-idealities on compressed sensing signal reconstruction in the random demodulator (RD) architecture. The random demodulator is a compressed sensing (CS) acquisition scheme capable of acquiring signals in continuous time. One of the main advantages of the system is the possibility to use off-the-shelf components to implement this sub-Nyquist framework. Low-pass filtering plays an important role in the RD analog acquisition process, which needs to be modeled carefully in the digital part of the compressive sensing reconstruction. Having a complete model of the analog front-end, CS algorithms conduct almost perfect reconstruction taking far less samples than for traditional Nyquist-rate sampling. This paper investigates reconstruction sensitivity to distortion in the impulse response of the low-pass filter caused by passive component value fluctuations. The authors simulate common CS recovery algorithms and show that the worst-case performance degradation due to filter component tolerances can be substantial, which requires special attention when designing reconstruction algorithms for RD.