Accurate and efficient modeling of random demodulation based compressive sensing systems with a general filter

Random demodulation provides a hardware-compact architecture for realizing compressive sensing systems. A random demodulator is realized by a mixer, with a random signal as the oscillator, and a low pass filter. In order to recover the original signal from the compressive sensing measurements, accurate modeling of the hardware components is needed. Typically, the reconstruction model assumes the low pass filter to be an ideal integrator. While this assumption is valid at low frequencies, it poses tremendous challenges at frequencies higher than 50MHz. In this paper, we provide an accurate and efficient model for the random demodulator that takes into account the actual structure of the filter. Using our model at reconstruction allows random demodulation for bandwidths extending to the GHz range, while, as we demonstrate, assuming an ideal integrator at reconstruction severely limits the system bandwidth.