Spectrum has valuable resource in wireless communication. In wireless communication some spectrum is waste due to uses of Cyclic Prefix (cp) in FFT multicarrier sampling. In place of FFT used DFT and wavelet transform function for removal of cyclic prefix. Wavelet based OFDM, particularly using DWT and WPT-OFDM as situations for Fourier-based OFDM with the focus on impulse noise effects. The authors begin by constructing the models of the inverse and forward transforms. They explain in detail each model and study the BER performance in two scenarios when varying the Poisson recurrence parameter from small to large. The wavelet based SOFDM (DWT-SOFDM and WPT-SOFDM) are assumed to have other normal bases and perfect reconstruction properties.