We report here on the utilization of signal in-phase-quadrature (I-Q) diagrams in a novel modulation classification (MC) technique. This MC technique is able to classify linear digital single-carrier modulations as well as multi-carrier modulations. The method uses the waveforms' I-Q diagrams and, by employing a combination of k-center and k-means algorithms, determines the type of modulation. Implementation and refinement of the novel single-carrier modulation classification technique using the I-Q diagrams are discussed in detail. Further, a model for classification of multi-carrier signals is presented, including Gaussianity, cyclostationarity, and autocorrelation tests for further extracting orthogonal frequency division multiplexing signal parameters. Finally, results of this method are presented and compared to other classification methods, and the considerations for implementing the method in hardware are briefly discussed. As a future direction of this research, the performance of the algorithm in fading channels is an interesting topic to pursue.