This research considers the problem of cooperatively identifying the active bands in a wideband spectrum using the sparse Fast Fourier Transform (sFFT). Existing research has focused primarily on Compressed Sensing (CS) and Multi-Coset (MC) sampling, but recent developments in the sFFT have shown that a sparsely occupied spectrum can be efficiently reconstructed using multiple co-prime analog-to-digital converters (ADC) that sample below the Nyquist rate. Specifically, this research utilizes the Robust Fast Fourier Aliasing-based Sparse Transform (R-FFAST) and extends this algorithm for use in cooperative wideband spectrum sensing (CWSS). Unlike previous approaches that implement the sFFT for spectrum sensing, the R-FFAST framework was developed and analyzed using the mutual coherence and the restricted isometry property (RIP) from CS theory. This leads to reliable support estimation in the presence of additive white Gaussian noise (AWGN) while mitigating the computational complexity of CS reconstruction algorithms. This research makes the following contributions. First, this research extends the signal model from single tones to multi-band signals with clustered support. Second, it shows that each stage in the R-FFAST front-end can be decomposed into individual nodes that form a fully distributed cooperative network. Lastly, this research empirically develops a constant false alarm rate (CFAR) detector that is used to identify the active frequency bins during the reconstruction process. The primary result of this research is showing that reliable spectrum detection is only possible when the average sampling rate of the cooperative network is greater than or equal to the sparsity of the spectrum. Simulation results are provided to demonstrate the effectiveness of the proposed framework and validate the findings of this research.