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In this tutorial article we review different multicarrier communication methods for the physical layer of cognitive radio systems. There, secondary users need to dynamically and reliably determine spectral holes, and transmit data in these resources without interfering with other parts of the frequency band. To satisfy the first, each SU has to be equipped with a spectrum analyzer. To satisfy the second, it is widely accepted that a multicarrier modulation technique should be adopted. Moreover, to maximize efficiency, it has been recognized that the side-lobes of each subcarrier band must be minimized. Much of the attention in the present literature emphasizes on the use of conventional OFDM, exploiting the fact that fast Fourier transform (FFT) as part of the OFDM modulator can also be used for channel sensing. Herein, we discuss the performance of OFDM, and also introduce filterbanks for multicarrier communication and spectral analysis in a CR setting. Moreover, the multitaper method has been proposed as an effective method for spectrum analysis. Our article provides an insight into the pros and cons of these technologies.