A method of and apparatus removing of a plurality of relatively narrow banded signals in a relatively wide banded input signal. The method involves and the apparatus provides for compressively sensing one relatively narrow banded signal in the relatively wide banded input signal and removing one relatively narrow banded signal from the relatively wide banded input signal before detecting and removing another relatively narrow banded signal in the relatively wide banded input signal, the step of and apparatus for compressing sensing occurring with respect to both (i) the input signal with the previously detected narrow banded signals removed therefrom and (ii) a frequency shifted version of (i).