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The primary task in any cognitive radio (CR) network is to dynamically explore the radio spectrum and reliably determine portion(s) of the frequency band that may be used for the communication link(s). Accordingly, each CR node in the network has to be equipped with a spectrum analyzer. In this paper, we propose filter banks as a tool for spectrum sensing in CR systems. Various choices of filter banks are suggested and their performance are evaluated theoretically and through numerical examples. Moreover, the proposed spectrum analyzer is contrasted with the Thomson's multitaper (MT) method - a method that in the recent literature has been recognized as the best choice for spectrum sensing in CR systems. A novel derivation of the MT method that facilitates our comparisons as well as reveals an important aspect of the MT method that has been less emphasized in the recent literature is also presented.