This paper presents cepstral analysis of OFDM signals. Cepstrum can reveal periodicities in a signal and has been widely used in audio and speech processing applications. In this work, the focus is on cepstrum based detection and classification of OFDM signals for cognitive radio applications such as flexible spectrum reuse and coexistence of heterogeneous networks. Two cepstrum based sensing schemes formulated as hypothesis testing are proposed. The distributions of the test statistics are derived under the null hypothesis so that the thresholds for the Neyman-Pearson detectors can be computed analytically. These cepstrum based schemes are compared to the traditional energy detector. First scheme is robust to noise uncertainty which is a clear benefit when compared to the energy detector. On the other hand, the second cepstrum based scheme has performance similar to the energy detection. Later, it is shown that the cepstral analysis can be used to estimate parameters of OFDM waveforms such as number of samples in data and cyclic prefix (CP) parts of an OFDM symbol. These features can be used to distinguish among different OFDM waveforms, which is not possible with energy detection.