An orthosis embedded with a surface electromyography (sEMG) measurement system, integrated with metal-polymer composite fibers, was used to monitor the electrical activity of the forearm muscles during movement. The comfortable and noninvasive sEMG system was developed for long term monitoring during rehabilitation. Wavelets were used to denoise and compress the raw biosignals. The focus here is a comparison of the usefulness of the Haars and Daubechies wavelets in this process, using the Discrete Wavelet Transform (DWT) version of Wavelet Package Transform (WPT). A denoising algorithm is proposed to detect unavoidable measured noise in the acquired data, which uses a seminorm to define the noise. Using this norm it is possible to rearrange the wavelet basis, which can illuminate the differences between the coherent and incoherent parts of the sequence, where incoherent refers to the part of the signal that has either no information or contradictory information. In effect, the procedure looks for the subspace characterized either by small components or by opposing components in the wavelet domain. The proposed method is general, can be applied to any low frequency signal processing, and was built with wavelet algorithms from the WaveLab 850 library of the Stanford University (USA).