Implicit notch filtering in compressed sensing by spectral shaping of sensing matrix

Compressed Sensing (CS) has recently emerged as an interesting and effective way to sample an input signal and at the same time compress it (i.e., reduce the number of measurements for the correct signal reconstruction with respect to the standard Nyquist approach). We show here that CS can be used also to exploit some operations typically performed by the preceding signal conditioning stage (sometimes, by a post-processing stage). In detail, we show that CS can be used to filter environmental disturbances exactly like a notch filter. Furthermore, this solution presents advantages in terms of input signal distortion with respect to the classical notch filter approach. An example on electrocardiographic signal is presented as case study.