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This paper presents a novel digital modulation classification system for cognitive radios using only temporal waveform features. Temporal features extraction is desirable for cognitive radios because it is easy to implement them compared to the extraction of other features types such as spectral features. The features used for classification are extracted from instantaneous amplitude and phase of the digitized intermediate frequency signal. A hierarchical approach is used to first make separations into intermediate subclasses, where some of the subclasses can consist of more than one modulation type. Then a second classifier is used to discriminate between higher order modulation schemes using additional features. Compared to alternative methods, the simulation results show the overall effectiveness of the proposed method in the presence of noise, especially for higher order digital modulations. Particularly, the overall success rate for the classification of seven common digital modulation schemes exceeds 95% at signal to noise ratios ranging from 10 dB to 80 dB.