This brief presents a novel algorithm to perform cooperative wideband spectrum sensing (CWSS) for cognitive radios (CRs). The proposed algorithm is based on a sub-Nyquist version of the sparse fast Fourier transform (sFFT) algorithm, and it is executed cooperatively by using M identical nodes. In this case, we designed a CWSS circuit based on the proposed algorithm that implements the main functional procedures of the sub-Nyquist sFFT algorithm by using multi-coset sampling and relatively prime sampling rates. According to the verification results, the proposed circuit based on the designed CWSS algorithm is suitable for implementing CWSS in CRs for sparse spectra composed of highly noisy multiband signals, and it improves the performance of previous sub-Nyquist sFFT algorithm and previous sFFT hardware implementation.