Dynamic spectrum access has been proposed as a solution to face spectrum scarcity, on one hand, and the high demand for accessing it, on the other hand. Cognitive radio has been suggested as a key technology to deal with these issues, using the spectrum opportunistically, in changing environments. Users of cognitive radio, as the secondaries, need to sense the presence of primary or licensed users periodically and quickly and if there were no activity, acquire the license of using the frequency band. In order to achieve higher throughput for secondary users and also limit interference with primary users by quick evacuation of the channel at the moment of their presence, the sensing cycle should be short and effective. However, the detection performance is at risk due to multi-path fading and uncertainty about the power of disturbance. In order to circumvent these effects, cooperative sensing is discussed as an effective method for providing spatial diversity. However, cooperative sensing imposes cooperative overhead. Overhead, refers to issues like additional sensing time, report delay, energy consumption, etc. In this thesis, spectrum sensing based on wavelet transform is studied, as a method for the detection of active primary user or spectrum hole with energy approach. After denoising the signal that is received by wavelet, spectrum sensing is examinedin the presence of generalized Gaussian noise. In another arrangement, with the assumption of the knowledge of rimary signal power spectrum and using the concepts of wavelet in orthonormal multiresolution space, determination of a wavelet with amplitude response corresponding to the square root of the spe ctrum is pursued. This wavelet is applied as a band ass filter to the received signal in both individual and cooperative sensing during the sensing period prior to energy detection. The results of simulations indicate that in both cases, there is a significant improvement in spectrum sensing performance in comparison with the conventional energy detection. Denoising of received signal by wavelet transform method indicates better performance in comparison with the received signal transition through the filter matching on the square root of the signal spectrum. Keywords: Cognitive radio, spectrum sensing, energy detection, non-gaussian noise, wavelet transform, primary power spectrum