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In this paper we demonstrate the operation of a Wavelet Packet based multi-carrier modulation (WPMCM) transceiver for Dynamic Spectrum Access. The wavelet packet (WP) bases are derived from multistage tree-structured paraunitary filter banks. To enable the WPMCM Cognitive Radio (CR) system to co-exist with other Licensed Users (LU) a common spectrum pool is maintained and the WPMCM transmission waveform characteristics are shaped to communicate in the idle time-frequency gaps of the licensed user. This is achieved by dynamically vacating WP carriers in and near the region of the licensed user spectrum. Furthermore, a spectrum estimation unit is tagged to the WPMCM transceiver structure by exploiting the filter bank infrastructure used for Discrete Wavelet Packet Transform implementation. Thus spectrum analysis is done at no additional cost. In the studies, two types of LUs are employed, namely, partial band and multiple tone. The simulation results show that in the presence of LU, the proposed spectrum adaptation method offers significant BER improvements allowing the CR to operate invisibly to the LU.