Abstract: A method and apparatus for sampling a high bandwidth analog signal includes: splitting the high bandwidth analog signal into N parallel channels; randomly demodulating each of the signals; sampling each demodulated signal using a sub-Nyquist sampling rate; combining each sampled signal into a sub-Nyquist signal; compressive sensing the combined sub-Nyquist signal to estimate missing samples of a full Nyquist rate uniform sample set X(n); convolving X(n) with N analysis filters, each analysis filter having a different coefficient; decimating output of each analysis filter using decimation ratios of M:1 to generate a sub-banded signal set Yi (n), i=1, . . . , N; processing the sub-banded signal set; up-sampling each processed sub-band signal by M; convolving each up-sampled sub-band signal with a corresponding synthesis filter; and combining two or more of the convolved signals to generate a non-uniform spectral partitioning of the high bandwidth analog signal.