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Auction is widely applied in wireless communication for spectrum allocation. Most of prior works have assumed that all spectrums are identical. In reality, however, spectrums provided by different owners have distinctive characteristics in both spacial and frequency domains. Spectrum availability also varies in different geo-locations. Furthermore, frequency diversity may cause non-identical conflict relationships among spectrum buyers since different frequencies have distinct communication ranges. Under such a scenario, existing spectrum auction schemes cannot provide truthfulness or efficiency. In this paper, we propose a Truthful double Auction mechanism for HEterogeneous Spectrum, called TAHES, which allows buyers to explicitly express their personalized preferences for heterogeneous spectrums and also addresses the problem of interference graph variation. We prove that TAHES has nice economic properties including truthfulness, individual rationality and budget balance. Results from extensive simulation studies demonstrate the truthfulness, effectiveness and efficiency of TAHES.